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Properties

Label 1334.2.f
Level $1334$
Weight $2$
Character orbit 1334.f
Rep. character $\chi_{1334}(505,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(i)\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 368 120 248
Cusp forms 352 120 232
Eisenstein series 16 0 16

Trace form

\( 120 q + O(q^{10}) \) \( 120 q - 120 q^{16} + 16 q^{23} - 16 q^{24} + 88 q^{25} + 8 q^{26} + 48 q^{27} + 8 q^{29} + 16 q^{31} - 136 q^{36} - 16 q^{39} + 40 q^{41} + 12 q^{46} + 32 q^{47} - 104 q^{49} + 16 q^{50} + 32 q^{52} - 64 q^{54} - 48 q^{55} - 64 q^{59} + 12 q^{69} + 40 q^{70} + 64 q^{73} - 24 q^{75} - 24 q^{77} + 48 q^{78} - 88 q^{81} + 32 q^{82} - 72 q^{85} - 24 q^{87} + 32 q^{94} + 40 q^{95} - 16 q^{98} + O(q^{100}) \)

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

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