Properties

Label 1148.2.f
Level $1148$
Weight $2$
Character orbit 1148.f
Rep. character $\chi_{1148}(83,\cdot)$
Character field $\Q$
Dimension $160$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 172 160 12
Cusp forms 164 160 4
Eisenstein series 8 0 8

Trace form

\( 160q - 2q^{2} + 2q^{4} - 2q^{8} + 160q^{9} + O(q^{10}) \) \( 160q - 2q^{2} + 2q^{4} - 2q^{8} + 160q^{9} - 18q^{14} - 6q^{16} - 30q^{18} - 8q^{21} + 8q^{22} - 176q^{25} + 16q^{28} - 16q^{29} + 32q^{30} - 22q^{32} + 10q^{36} - 32q^{37} - 12q^{42} - 16q^{44} - 4q^{46} + 16q^{49} + 50q^{50} + 32q^{53} - 26q^{56} - 32q^{57} - 44q^{58} + 24q^{60} - 10q^{64} + 16q^{65} + 6q^{70} + 48q^{72} + 2q^{74} - 32q^{77} + 66q^{78} + 144q^{81} - 50q^{84} + 48q^{85} + 40q^{86} - 4q^{88} + 22q^{92} - 16q^{93} - 78q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1148, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)