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Properties

Label 1334.2.x
Level $1334$
Weight $2$
Character orbit 1334.x
Rep. character $\chi_{1334}(11,\cdot)$
Character field $\Q(\zeta_{308})$
Dimension $7200$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.x (of order \(308\) and degree \(120\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{308})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 22080 7200 14880
Cusp forms 21120 7200 13920
Eisenstein series 960 0 960

Trace form

\( 7200 q + O(q^{10}) \) \( 7200 q - 120 q^{16} - 44 q^{19} + 132 q^{21} - 12 q^{23} + 40 q^{24} - 240 q^{25} - 36 q^{26} - 252 q^{27} - 92 q^{29} - 40 q^{31} - 112 q^{35} - 80 q^{36} + 72 q^{39} + 40 q^{41} - 88 q^{43} + 12 q^{46} + 88 q^{47} - 216 q^{49} + 16 q^{50} - 616 q^{51} + 32 q^{52} + 24 q^{54} + 128 q^{55} - 44 q^{56} - 64 q^{59} + 176 q^{66} - 44 q^{69} + 40 q^{70} - 56 q^{71} - 24 q^{73} - 24 q^{75} - 1064 q^{77} - 216 q^{78} - 312 q^{81} + 32 q^{82} + 264 q^{83} + 44 q^{84} + 176 q^{85} - 156 q^{87} - 44 q^{89} - 84 q^{92} + 32 q^{94} - 272 q^{95} - 44 q^{97} + 72 q^{98} + 132 q^{99} + O(q^{100}) \)

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

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