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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

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

Display 100 coefficients 10 coefficients

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

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