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Properties

Label 1334.2.m
Level $1334$
Weight $2$
Character orbit 1334.m
Rep. character $\chi_{1334}(173,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $600$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.m (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 1840 600 1240
Cusp forms 1760 600 1160
Eisenstein series 80 0 80

Trace form

\( 600 q + 60 q^{4} - 4 q^{5} + 8 q^{6} + 68 q^{9} + O(q^{10}) \) \( 600 q + 60 q^{4} - 4 q^{5} + 8 q^{6} + 68 q^{9} + 16 q^{13} - 60 q^{16} + 4 q^{20} + 40 q^{22} - 76 q^{23} - 8 q^{24} + 28 q^{25} + 14 q^{29} + 16 q^{30} - 24 q^{33} - 8 q^{34} + 8 q^{35} - 68 q^{36} + 12 q^{38} - 16 q^{42} - 112 q^{45} - 192 q^{49} + 104 q^{51} - 16 q^{52} + 12 q^{53} + 60 q^{54} + 52 q^{57} - 16 q^{58} - 24 q^{59} - 108 q^{62} - 164 q^{63} + 60 q^{64} + 68 q^{67} + 16 q^{71} - 148 q^{74} + 164 q^{78} - 4 q^{80} - 108 q^{81} - 88 q^{82} + 52 q^{83} + 24 q^{86} + 114 q^{87} + 4 q^{88} - 8 q^{91} - 12 q^{92} - 56 q^{93} + 8 q^{94} + 8 q^{96} + O(q^{100}) \)

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

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