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Properties

Label 1334.2.o
Level $1334$
Weight $2$
Character orbit 1334.o
Rep. character $\chi_{1334}(137,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $720$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.o (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 2208 720 1488
Cusp forms 2112 720 1392
Eisenstein series 96 0 96

Trace form

\( 720 q + O(q^{10}) \) \( 720 q + 120 q^{16} + 12 q^{23} - 40 q^{24} - 200 q^{25} - 8 q^{26} + 120 q^{27} + 48 q^{29} + 40 q^{31} + 112 q^{35} + 80 q^{36} + 16 q^{39} - 40 q^{41} - 12 q^{46} - 88 q^{47} + 216 q^{49} - 16 q^{50} - 32 q^{52} + 64 q^{54} + 48 q^{55} + 64 q^{59} + 44 q^{69} - 40 q^{70} + 56 q^{71} - 64 q^{73} + 24 q^{75} - 256 q^{77} - 48 q^{78} + 312 q^{81} - 32 q^{82} - 264 q^{85} + 24 q^{87} + 84 q^{92} - 32 q^{94} + 184 q^{95} + 16 q^{98} + O(q^{100}) \)

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

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