Properties

Label 6930.2.a
Level $6930$
Weight $2$
Character orbit 6930.a
Rep. character $\chi_{6930}(1,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $65$
Sturm bound $3456$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6930.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 65 \)
Sturm bound: \(3456\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(13\), \(17\), \(19\), \(23\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6930))\).

Total New Old
Modular forms 1760 100 1660
Cusp forms 1697 100 1597
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.
\(+\)\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(42\)
Minus space\(-\)\(58\)

Trace form

\( 100 q + 100 q^{4} + O(q^{10}) \) \( 100 q + 100 q^{4} + 100 q^{16} - 16 q^{17} - 16 q^{19} - 4 q^{22} - 24 q^{23} + 100 q^{25} - 8 q^{26} - 16 q^{29} - 8 q^{31} - 24 q^{37} - 24 q^{38} - 40 q^{47} + 100 q^{49} + 24 q^{53} - 16 q^{59} - 32 q^{61} + 16 q^{62} + 100 q^{64} - 16 q^{65} + 24 q^{67} - 16 q^{68} - 4 q^{70} - 32 q^{71} - 24 q^{74} - 16 q^{76} + 8 q^{77} + 40 q^{79} + 32 q^{82} + 16 q^{83} - 16 q^{86} - 4 q^{88} + 8 q^{89} + 16 q^{91} - 24 q^{92} + 48 q^{94} + 24 q^{95} + 40 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6930))\) 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
6930.2.a.a 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.b 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.c 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.d 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.e 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.f 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.g 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.h 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.i 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.j 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.k 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.l 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.m 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.n 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.o 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.p 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.q 6930.a 1.a $1$ $55.336$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.r 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.s 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.t 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.u 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.v 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.w 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.x 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.y 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.z 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.ba 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.bb 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bc 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bd 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.be 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bf 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bg 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bh 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bi 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bj 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bk 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bl 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bm 6930.a 1.a $1$ $55.336$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bn 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-2\) \(-2\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.bo 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(-2\) \(2\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.bp 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(-2\) \(2\) $+$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.bq 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.br 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bs 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(2\) \(-2\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bt 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bu 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bv 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bw 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(-2\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.bx 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{17}) \) None \(2\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.by 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(-2\) \(-2\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.bz 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.ca 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.cb 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.cc 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(2\) \(2\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.cd 6930.a 1.a $2$ $55.336$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.ce 6930.a 1.a $3$ $55.336$ 3.3.316.1 None \(-3\) \(0\) \(-3\) \(-3\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.cf 6930.a 1.a $3$ $55.336$ 3.3.316.1 None \(-3\) \(0\) \(-3\) \(-3\) $+$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.cg 6930.a 1.a $3$ $55.336$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(-3\) \(-3\) $+$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.ch 6930.a 1.a $3$ $55.336$ 3.3.148.1 None \(-3\) \(0\) \(-3\) \(3\) $+$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.ci 6930.a 1.a $3$ $55.336$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(3\) \(3\) $+$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.cj 6930.a 1.a $3$ $55.336$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(-3\) \(3\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.ck 6930.a 1.a $3$ $55.336$ \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(3\) \(-3\) $-$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.cl 6930.a 1.a $3$ $55.336$ 3.3.892.1 None \(3\) \(0\) \(3\) \(-3\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.cm 6930.a 1.a $3$ $55.336$ 3.3.316.1 None \(3\) \(0\) \(3\) \(-3\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6930))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6930)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1386))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3465))\)\(^{\oplus 2}\)