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Properties

Label 1148.2.p
Level $1148$
Weight $2$
Character orbit 1148.p
Rep. character $\chi_{1148}(411,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 344 320 24
Cusp forms 328 320 8
Eisenstein series 16 0 16

Trace form

\( 320 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 160 q^{9} + O(q^{10}) \) \( 320 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 160 q^{9} - 30 q^{12} - 6 q^{14} - 18 q^{16} - 16 q^{21} + 16 q^{22} + 152 q^{25} + 32 q^{28} - 32 q^{29} + 16 q^{30} - 8 q^{32} - 24 q^{33} + 20 q^{36} + 8 q^{37} - 54 q^{42} - 26 q^{44} + 4 q^{46} - 16 q^{49} - 8 q^{50} + 54 q^{52} - 8 q^{53} - 30 q^{54} + 2 q^{56} + 80 q^{57} - 4 q^{58} - 24 q^{60} + 24 q^{61} - 20 q^{64} - 16 q^{65} + 30 q^{68} + 66 q^{70} + 18 q^{72} - 72 q^{73} - 2 q^{74} - 16 q^{77} - 96 q^{78} + 60 q^{80} - 144 q^{81} + 44 q^{84} - 48 q^{85} + 44 q^{86} + 4 q^{88} - 64 q^{92} - 8 q^{93} - 102 q^{96} + 60 q^{98} + O(q^{100}) \)

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

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