Properties

Label 9240.2.a
Level $9240$
Weight $2$
Character orbit 9240.a
Rep. character $\chi_{9240}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $63$
Sturm bound $4608$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 9240 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9240.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 63 \)
Sturm bound: \(4608\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(13\), \(17\), \(19\), \(23\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9240))\).

Total New Old
Modular forms 2336 120 2216
Cusp forms 2273 120 2153
Eisenstein series 63 0 63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(52\)
Minus space\(-\)\(68\)

Trace form

\( 120 q + 120 q^{9} + O(q^{10}) \) \( 120 q + 120 q^{9} - 16 q^{23} + 120 q^{25} - 16 q^{31} - 16 q^{37} - 32 q^{41} - 16 q^{43} - 16 q^{47} + 120 q^{49} - 16 q^{51} - 32 q^{53} - 32 q^{59} + 64 q^{71} - 32 q^{73} - 48 q^{79} + 120 q^{81} + 64 q^{83} - 32 q^{87} + 48 q^{89} - 16 q^{91} - 16 q^{93} - 16 q^{95} + 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9240))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 7 11
9240.2.a.a 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.b 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
9240.2.a.c 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.d 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.e 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.f 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.g 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
9240.2.a.h 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
9240.2.a.i 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.j 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
9240.2.a.k 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.l 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
9240.2.a.m 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
9240.2.a.n 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-q^{15}+\cdots\)
9240.2.a.o 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
9240.2.a.p 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $+$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
9240.2.a.q 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.r 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.s 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $+$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.t 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
9240.2.a.u 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.v 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.w 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.x 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.y 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
9240.2.a.z 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{15}+\cdots\)
9240.2.a.ba 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
9240.2.a.bb 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
9240.2.a.bc 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.bd 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
9240.2.a.be 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
9240.2.a.bf 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.bg 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
9240.2.a.bh 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
9240.2.a.bi 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
9240.2.a.bj 9240.a 1.a $1$ $73.782$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.bk 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.bl 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.bm 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-2\) \(2\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2\beta q^{13}+\cdots\)
9240.2.a.bn 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(2\) \(-2\) $-$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-2\beta q^{13}+\cdots\)
9240.2.a.bo 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(-2\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+(-3+\cdots)q^{13}+\cdots\)
9240.2.a.bp 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{73}) \) None \(0\) \(-2\) \(2\) \(2\) $+$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.bq 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(2\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-\beta q^{13}+\cdots\)
9240.2.a.br 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{41}) \) None \(0\) \(2\) \(-2\) \(2\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-q^{15}+\cdots\)
9240.2.a.bs 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-2\beta q^{13}+\cdots\)
9240.2.a.bt 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+(2+\beta )q^{13}+\cdots\)
9240.2.a.bu 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
9240.2.a.bv 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(2\) \(2\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.bw 9240.a 1.a $2$ $73.782$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(2\) $+$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
9240.2.a.bx 9240.a 1.a $3$ $73.782$ 3.3.2300.1 None \(0\) \(-3\) \(-3\) \(3\) $+$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
9240.2.a.by 9240.a 1.a $3$ $73.782$ 3.3.6616.1 None \(0\) \(-3\) \(3\) \(3\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
9240.2.a.bz 9240.a 1.a $3$ $73.782$ 3.3.4860.1 None \(0\) \(3\) \(-3\) \(3\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)
9240.2.a.ca 9240.a 1.a $4$ $73.782$ 4.4.13968.1 None \(0\) \(-4\) \(4\) \(-4\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots\)
9240.2.a.cb 9240.a 1.a $4$ $73.782$ 4.4.16448.2 None \(0\) \(-4\) \(4\) \(4\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-\beta _{2}q^{13}+\cdots\)
9240.2.a.cc 9240.a 1.a $4$ $73.782$ 4.4.40864.1 None \(0\) \(4\) \(-4\) \(-4\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
9240.2.a.cd 9240.a 1.a $4$ $73.782$ 4.4.30056.1 None \(0\) \(4\) \(-4\) \(-4\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-\beta _{2}q^{13}+\cdots\)
9240.2.a.ce 9240.a 1.a $4$ $73.782$ 4.4.19664.1 None \(0\) \(4\) \(-4\) \(4\) $+$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+\beta _{1}q^{13}+\cdots\)
9240.2.a.cf 9240.a 1.a $4$ $73.782$ 4.4.19664.1 None \(0\) \(4\) \(4\) \(-4\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots\)
9240.2.a.cg 9240.a 1.a $4$ $73.782$ 4.4.11324.1 None \(0\) \(4\) \(4\) \(-4\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+(1+\beta _{2}+\cdots)q^{13}+\cdots\)
9240.2.a.ch 9240.a 1.a $5$ $73.782$ 5.5.2245192.1 None \(0\) \(-5\) \(-5\) \(-5\) $+$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+\beta _{2}q^{13}+\cdots\)
9240.2.a.ci 9240.a 1.a $5$ $73.782$ 5.5.1457888.1 None \(0\) \(-5\) \(-5\) \(-5\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+(1-\beta _{4})q^{13}+\cdots\)
9240.2.a.cj 9240.a 1.a $5$ $73.782$ 5.5.9229792.1 None \(0\) \(-5\) \(-5\) \(5\) $-$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
9240.2.a.ck 9240.a 1.a $6$ $73.782$ 6.6.235324384.1 None \(0\) \(6\) \(6\) \(6\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+(1-\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(924))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1848))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4620))\)\(^{\oplus 2}\)