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Properties

Label 1148.2.bi
Level $1148$
Weight $2$
Character orbit 1148.bi
Rep. character $\chi_{1148}(9,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
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.bi (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 696 112 584
Cusp forms 648 112 536
Eisenstein series 48 0 48

Trace form

\( 112 q + O(q^{10}) \) \( 112 q - 4 q^{11} + 12 q^{15} - 6 q^{17} + 4 q^{19} + 56 q^{25} + 12 q^{27} + 8 q^{29} + 8 q^{31} - 4 q^{35} - 28 q^{37} - 16 q^{41} - 40 q^{45} + 8 q^{47} - 28 q^{51} + 26 q^{53} + 4 q^{55} - 40 q^{57} + 32 q^{59} - 34 q^{63} - 12 q^{65} - 20 q^{67} - 68 q^{69} - 64 q^{71} - 10 q^{75} - 18 q^{79} + 64 q^{81} - 112 q^{83} + 72 q^{85} + 38 q^{89} - 20 q^{93} - 8 q^{95} - 28 q^{97} + 80 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1148, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(574, [\chi])\)\(^{\oplus 2}\)