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Properties

Label 1334.2.q
Level $1334$
Weight $2$
Character orbit 1334.q
Rep. character $\chi_{1334}(17,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1200$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.q (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1334, [\chi])\).

Total New Old
Modular forms 3680 1200 2480
Cusp forms 3520 1200 2320
Eisenstein series 160 0 160

Trace form

\( 1200 q + O(q^{10}) \) \( 1200 q + 120 q^{16} + 44 q^{19} - 132 q^{21} - 16 q^{23} + 16 q^{24} - 264 q^{25} + 36 q^{26} + 84 q^{27} + 36 q^{29} - 16 q^{31} + 136 q^{36} - 72 q^{39} - 40 q^{41} + 88 q^{43} - 12 q^{46} - 32 q^{47} + 104 q^{49} - 16 q^{50} - 32 q^{52} - 24 q^{54} - 128 q^{55} + 44 q^{56} + 64 q^{59} - 176 q^{66} - 12 q^{69} - 40 q^{70} + 24 q^{73} + 24 q^{75} - 196 q^{77} + 216 q^{78} + 88 q^{81} - 32 q^{82} - 264 q^{83} - 44 q^{84} + 160 q^{85} + 156 q^{87} + 44 q^{89} - 32 q^{94} + 48 q^{95} + 44 q^{97} - 72 q^{98} - 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1334, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1334, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1334, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(667, [\chi])\)\(^{\oplus 2}\)