Properties

Label 1148.2.y
Level $1148$
Weight $2$
Character orbit 1148.y
Rep. character $\chi_{1148}(407,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $504$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.y (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1148, [\chi])\).

Total New Old
Modular forms 688 504 184
Cusp forms 656 504 152
Eisenstein series 32 0 32

Trace form

\( 504q - 24q^{6} - 16q^{9} + O(q^{10}) \) \( 504q - 24q^{6} - 16q^{9} - 8q^{12} + 56q^{17} + 8q^{29} - 32q^{30} + 40q^{32} - 80q^{33} - 40q^{34} + 24q^{36} + 40q^{41} - 80q^{42} + 40q^{52} - 8q^{53} + 72q^{54} + 40q^{60} - 40q^{61} - 72q^{62} - 152q^{74} - 104q^{78} - 80q^{80} + 32q^{85} + 8q^{88} - 16q^{89} - 152q^{92} - 200q^{94} - 128q^{96} - 40q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1148, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1148, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1148, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 2}\)