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Properties

Label 1148.2.ca
Level $1148$
Weight $2$
Character orbit 1148.ca
Rep. character $\chi_{1148}(15,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $2016$
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.ca (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 2752 2016 736
Cusp forms 2624 2016 608
Eisenstein series 128 0 128

Trace form

\( 2016 q + 24 q^{6} + 16 q^{9} + O(q^{10}) \) \( 2016 q + 24 q^{6} + 16 q^{9} + 8 q^{12} - 56 q^{17} - 8 q^{29} + 32 q^{30} - 40 q^{32} + 80 q^{33} + 40 q^{34} - 24 q^{36} - 40 q^{41} + 80 q^{42} - 40 q^{52} + 8 q^{53} - 72 q^{54} - 40 q^{60} + 40 q^{61} + 72 q^{62} - 160 q^{66} - 360 q^{72} - 88 q^{74} - 296 q^{78} - 320 q^{80} - 32 q^{85} - 400 q^{86} - 408 q^{88} + 16 q^{89} - 88 q^{92} - 160 q^{94} + 128 q^{96} + 40 q^{97} + O(q^{100}) \)

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

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