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Properties

Label 6762.2.a
Level $6762$
Weight $2$
Character orbit 6762.a
Rep. character $\chi_{6762}(1,\cdot)$
Character field $\Q$
Dimension $150$
Newform subspaces $74$
Sturm bound $2688$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6762.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 74 \)
Sturm bound: \(2688\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6762))\).

Total New Old
Modular forms 1376 150 1226
Cusp forms 1313 150 1163
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.

\(2\)\(3\)\(7\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(12\)
\(+\)\(+\)\(+\)\(-\)$-$\(8\)
\(+\)\(+\)\(-\)\(+\)$-$\(7\)
\(+\)\(+\)\(-\)\(-\)$+$\(10\)
\(+\)\(-\)\(+\)\(+\)$-$\(11\)
\(+\)\(-\)\(+\)\(-\)$+$\(7\)
\(+\)\(-\)\(-\)\(+\)$+$\(8\)
\(+\)\(-\)\(-\)\(-\)$-$\(11\)
\(-\)\(+\)\(+\)\(+\)$-$\(9\)
\(-\)\(+\)\(+\)\(-\)$+$\(9\)
\(-\)\(+\)\(-\)\(+\)$+$\(9\)
\(-\)\(+\)\(-\)\(-\)$-$\(12\)
\(-\)\(-\)\(+\)\(+\)$+$\(6\)
\(-\)\(-\)\(+\)\(-\)$-$\(14\)
\(-\)\(-\)\(-\)\(+\)$-$\(13\)
\(-\)\(-\)\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(65\)
Minus space\(-\)\(85\)

Trace form

\( 150 q + 2 q^{2} - 2 q^{3} + 150 q^{4} + 4 q^{5} - 2 q^{6} + 2 q^{8} + 150 q^{9} + O(q^{10}) \) \( 150 q + 2 q^{2} - 2 q^{3} + 150 q^{4} + 4 q^{5} - 2 q^{6} + 2 q^{8} + 150 q^{9} - 2 q^{12} - 4 q^{13} - 4 q^{15} + 150 q^{16} - 4 q^{17} + 2 q^{18} - 12 q^{19} + 4 q^{20} - 12 q^{22} - 2 q^{24} + 146 q^{25} + 12 q^{26} - 2 q^{27} - 4 q^{29} - 16 q^{31} + 2 q^{32} + 4 q^{33} + 12 q^{34} + 150 q^{36} + 32 q^{37} - 8 q^{38} + 36 q^{39} - 12 q^{41} + 60 q^{43} + 4 q^{45} + 4 q^{46} - 24 q^{47} - 2 q^{48} + 86 q^{50} + 8 q^{51} - 4 q^{52} + 76 q^{53} - 2 q^{54} + 16 q^{55} + 60 q^{57} + 68 q^{58} + 8 q^{59} - 4 q^{60} + 24 q^{61} + 8 q^{62} + 150 q^{64} + 40 q^{65} + 20 q^{67} - 4 q^{68} - 4 q^{69} - 40 q^{71} + 2 q^{72} + 12 q^{73} + 52 q^{74} + 2 q^{75} - 12 q^{76} - 4 q^{78} + 4 q^{80} + 150 q^{81} - 4 q^{82} + 24 q^{83} + 72 q^{85} - 16 q^{86} + 12 q^{87} - 12 q^{88} - 4 q^{89} + 32 q^{93} + 8 q^{94} - 24 q^{95} - 2 q^{96} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6762))\) 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 7 23
6762.2.a.a 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.b 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.c 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.d 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.e 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.f 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.g 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.h 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.i 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.j 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.k 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.l 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.m 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.n 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.o 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
6762.2.a.p 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.q 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.r 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.s 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.t 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(3\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.u 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(3\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.v 6762.a 1.a $1$ $53.995$ \(\Q\) None \(-1\) \(1\) \(4\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.w 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(-1\) \(-4\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.x 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.y 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.z 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
6762.2.a.ba 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
6762.2.a.bb 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.bc 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.bd 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(-1\) \(3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.be 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(-1\) \(3\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.bf 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bg 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bh 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bi 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bj 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
6762.2.a.bk 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
6762.2.a.bl 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bm 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bn 6762.a 1.a $1$ $53.995$ \(\Q\) None \(1\) \(1\) \(4\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.bo 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.bp 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.bq 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.br 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.bs 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
6762.2.a.bt 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
6762.2.a.bu 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
6762.2.a.bv 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
6762.2.a.bw 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.bx 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.by 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.bz 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-4\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.ca 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
6762.2.a.cb 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
6762.2.a.cc 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
6762.2.a.cd 6762.a 1.a $2$ $53.995$ \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(3\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
6762.2.a.ce 6762.a 1.a $3$ $53.995$ 3.3.3132.1 None \(-3\) \(-3\) \(3\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.cf 6762.a 1.a $3$ $53.995$ 3.3.3132.1 None \(-3\) \(3\) \(-3\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.cg 6762.a 1.a $4$ $53.995$ 4.4.138768.1 None \(-4\) \(-4\) \(2\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.ch 6762.a 1.a $4$ $53.995$ 4.4.138768.1 None \(-4\) \(4\) \(-2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{8}+\cdots\)
6762.2.a.ci 6762.a 1.a $4$ $53.995$ 4.4.2624.1 None \(4\) \(-4\) \(-8\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-2-\beta _{1})q^{5}-q^{6}+\cdots\)
6762.2.a.cj 6762.a 1.a $4$ $53.995$ 4.4.23252.1 None \(4\) \(-4\) \(-3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots\)
6762.2.a.ck 6762.a 1.a $4$ $53.995$ 4.4.10304.1 None \(4\) \(-4\) \(2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}-q^{6}+\cdots\)
6762.2.a.cl 6762.a 1.a $4$ $53.995$ 4.4.473376.1 None \(4\) \(-4\) \(2\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
6762.2.a.cm 6762.a 1.a $4$ $53.995$ 4.4.42048.1 None \(4\) \(-4\) \(4\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{2})q^{5}-q^{6}+\cdots\)
6762.2.a.cn 6762.a 1.a $4$ $53.995$ 4.4.16448.2 None \(4\) \(-4\) \(6\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)
6762.2.a.co 6762.a 1.a $4$ $53.995$ 4.4.16448.2 None \(4\) \(4\) \(-6\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}+q^{6}+\cdots\)
6762.2.a.cp 6762.a 1.a $4$ $53.995$ 4.4.42048.1 None \(4\) \(4\) \(-4\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}+q^{6}+\cdots\)
6762.2.a.cq 6762.a 1.a $4$ $53.995$ 4.4.10304.1 None \(4\) \(4\) \(-2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
6762.2.a.cr 6762.a 1.a $4$ $53.995$ 4.4.473376.1 None \(4\) \(4\) \(-2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
6762.2.a.cs 6762.a 1.a $4$ $53.995$ 4.4.23252.1 None \(4\) \(4\) \(3\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{3})q^{5}+q^{6}+\cdots\)
6762.2.a.ct 6762.a 1.a $4$ $53.995$ 4.4.2624.1 None \(4\) \(4\) \(8\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(2+\beta _{1})q^{5}+q^{6}+\cdots\)
6762.2.a.cu 6762.a 1.a $8$ $53.995$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-8\) \(-2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{7}q^{5}+q^{6}-q^{8}+\cdots\)
6762.2.a.cv 6762.a 1.a $8$ $53.995$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(8\) \(2\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{7}q^{5}-q^{6}-q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6762))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6762)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2254))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3381))\)\(^{\oplus 2}\)