Properties

Label 4800.2.a
Level $4800$
Weight $2$
Character orbit 4800.a
Rep. character $\chi_{4800}(1,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $74$
Sturm bound $1920$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4800 = 2^{6} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4800.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 74 \)
Sturm bound: \(1920\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4800))\).

Total New Old
Modular forms 1032 76 956
Cusp forms 889 76 813
Eisenstein series 143 0 143

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

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(10\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(33\)
Minus space\(-\)\(43\)

Trace form

\( 76 q + 76 q^{9} + O(q^{10}) \) \( 76 q + 76 q^{9} + 8 q^{13} + 8 q^{17} + 8 q^{21} - 16 q^{29} - 8 q^{37} + 8 q^{41} + 76 q^{49} - 16 q^{53} + 24 q^{61} + 16 q^{69} - 8 q^{73} - 64 q^{77} + 76 q^{81} - 8 q^{89} + 8 q^{93} + 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4800))\) 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
4800.2.a.a 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-5q^{7}+q^{9}-6q^{11}-3q^{13}+\cdots\)
4800.2.a.b 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-5q^{7}+q^{9}+6q^{11}+3q^{13}+\cdots\)
4800.2.a.c 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}-4q^{13}+8q^{19}+\cdots\)
4800.2.a.d 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots\)
4800.2.a.e 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}+4q^{13}-8q^{19}+\cdots\)
4800.2.a.f 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4800.2.a.g 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}+q^{9}-4q^{11}+7q^{13}+\cdots\)
4800.2.a.h 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}+q^{9}-5q^{13}+5q^{19}+\cdots\)
4800.2.a.i 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}+q^{9}+5q^{13}-5q^{19}+\cdots\)
4800.2.a.j 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}+q^{9}+4q^{11}-7q^{13}+\cdots\)
4800.2.a.k 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
4800.2.a.l 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
4800.2.a.m 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
4800.2.a.n 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
4800.2.a.o 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-6q^{11}-5q^{13}+\cdots\)
4800.2.a.p 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots\)
4800.2.a.q 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
4800.2.a.r 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-4q^{11}+6q^{13}+6q^{17}+\cdots\)
4800.2.a.s 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
4800.2.a.t 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
4800.2.a.u 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
4800.2.a.v 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-4q^{11}-3q^{13}+\cdots\)
4800.2.a.w 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-q^{13}-3q^{19}-q^{21}+\cdots\)
4800.2.a.x 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}+q^{13}+3q^{19}-q^{21}+\cdots\)
4800.2.a.y 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}+4q^{11}+3q^{13}+\cdots\)
4800.2.a.z 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
4800.2.a.ba 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
4800.2.a.bb 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
4800.2.a.bc 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots\)
4800.2.a.bd 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots\)
4800.2.a.be 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4800.2.a.bf 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots\)
4800.2.a.bg 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
4800.2.a.bh 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
4800.2.a.bi 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)
4800.2.a.bj 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}+4q^{11}+4q^{17}+\cdots\)
4800.2.a.bk 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots\)
4800.2.a.bl 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
4800.2.a.bm 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)
4800.2.a.bn 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}+4q^{11}-4q^{17}+\cdots\)
4800.2.a.bo 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4800.2.a.bp 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots\)
4800.2.a.bq 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
4800.2.a.br 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
4800.2.a.bs 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}+q^{9}+2q^{11}+3q^{13}+\cdots\)
4800.2.a.bt 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
4800.2.a.bu 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
4800.2.a.bv 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}-4q^{11}+3q^{13}+\cdots\)
4800.2.a.bw 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}-q^{13}+3q^{19}-q^{21}+\cdots\)
4800.2.a.bx 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+q^{13}-3q^{19}-q^{21}+\cdots\)
4800.2.a.by 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+4q^{11}-3q^{13}+\cdots\)
4800.2.a.bz 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
4800.2.a.ca 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
4800.2.a.cb 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
4800.2.a.cc 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
4800.2.a.cd 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+4q^{11}+6q^{13}+6q^{17}+\cdots\)
4800.2.a.ce 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}-6q^{11}+5q^{13}+\cdots\)
4800.2.a.cf 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots\)
4800.2.a.cg 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
4800.2.a.ch 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
4800.2.a.ci 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
4800.2.a.cj 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
4800.2.a.ck 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}+q^{9}-4q^{11}-7q^{13}+\cdots\)
4800.2.a.cl 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}+q^{9}-5q^{13}-5q^{19}+\cdots\)
4800.2.a.cm 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}+q^{9}+5q^{13}+5q^{19}+\cdots\)
4800.2.a.cn 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}+q^{9}+4q^{11}+7q^{13}+\cdots\)
4800.2.a.co 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
4800.2.a.cp 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}-4q^{13}-8q^{19}+\cdots\)
4800.2.a.cq 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots\)
4800.2.a.cr 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+4q^{13}+8q^{19}+\cdots\)
4800.2.a.cs 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+5q^{7}+q^{9}-6q^{11}+3q^{13}+\cdots\)
4800.2.a.ct 4800.a 1.a $1$ $38.328$ \(\Q\) None \(0\) \(1\) \(0\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+5q^{7}+q^{9}+6q^{11}-3q^{13}+\cdots\)
4800.2.a.cu 4800.a 1.a $2$ $38.328$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}+\beta q^{11}+\beta q^{13}+\cdots\)
4800.2.a.cv 4800.a 1.a $2$ $38.328$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-\beta q^{11}+\beta q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2400))\)\(^{\oplus 2}\)