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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
334.2.c.a 334.c 167.c $574$ $2.667$ None \(-7\) \(-2\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{83}]$
334.2.c.b 334.c 167.c $574$ $2.667$ None \(7\) \(2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{83}]$

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

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