Properties

Label 334.2.c
Level $334$
Weight $2$
Character orbit 334.c
Rep. character $\chi_{334}(3,\cdot)$
Character field $\Q(\zeta_{83})$
Dimension $1148$
Newform subspaces $2$
Sturm bound $84$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 334 = 2 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 334.c (of order \(83\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 167 \)
Character field: \(\Q(\zeta_{83})\)
Newform subspaces: \( 2 \)
Sturm bound: \(84\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(334, [\chi])\).

Total New Old
Modular forms 3608 1148 2460
Cusp forms 3280 1148 2132
Eisenstein series 328 0 328

Trace form

\( 1148q - 14q^{4} - 2q^{5} - 4q^{6} - 26q^{9} + O(q^{10}) \) \( 1148q - 14q^{4} - 2q^{5} - 4q^{6} - 26q^{9} - 2q^{10} - 16q^{11} - 14q^{13} - 12q^{14} - 28q^{15} - 14q^{16} - 28q^{17} - 8q^{18} - 16q^{19} - 2q^{20} - 48q^{21} - 4q^{22} - 28q^{23} - 4q^{24} - 30q^{25} - 18q^{26} - 36q^{27} - 28q^{29} - 20q^{30} - 20q^{31} - 56q^{33} - 12q^{34} - 80q^{35} - 26q^{36} - 26q^{37} - 16q^{38} - 60q^{39} - 2q^{40} - 68q^{41} - 36q^{42} - 38q^{43} - 16q^{44} - 74q^{45} - 32q^{46} - 40q^{47} - 42q^{49} - 32q^{50} - 68q^{51} - 14q^{52} - 66q^{53} - 28q^{54} - 60q^{55} - 12q^{56} - 76q^{57} - 78q^{59} - 28q^{60} - 52q^{61} - 40q^{62} - 64q^{63} - 14q^{64} - 56q^{65} - 32q^{66} - 54q^{67} - 28q^{68} - 80q^{69} - 40q^{70} - 68q^{71} - 8q^{72} - 36q^{73} - 30q^{74} - 80q^{75} - 16q^{76} - 120q^{77} - 52q^{78} - 80q^{79} - 2q^{80} - 102q^{81} - 28q^{82} - 94q^{83} - 48q^{84} - 116q^{85} - 34q^{86} - 148q^{87} - 4q^{88} - 112q^{89} - 78q^{90} - 96q^{91} - 28q^{92} - 88q^{93} - 68q^{94} - 152q^{95} - 4q^{96} - 88q^{97} - 32q^{98} - 184q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(334, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
334.2.c.a \(574\) \(2.667\) None \(-7\) \(-2\) \(-2\) \(-6\)
334.2.c.b \(574\) \(2.667\) None \(7\) \(2\) \(0\) \(6\)

Decomposition of \(S_{2}^{\mathrm{old}}(334, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(334, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(167, [\chi])\)\(^{\oplus 2}\)