Properties

Label 1148.2.cj
Level $1148$
Weight $2$
Character orbit 1148.cj
Rep. character $\chi_{1148}(17,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $896$
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.cj (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{120})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 5568 896 4672
Cusp forms 5184 896 4288
Eisenstein series 384 0 384

Trace form

\( 896q + 8q^{9} + O(q^{10}) \) \( 896q + 8q^{9} - 24q^{15} - 36q^{17} + 24q^{19} + 8q^{21} - 32q^{29} - 60q^{33} + 40q^{35} + 36q^{37} - 16q^{43} - 24q^{47} - 8q^{49} + 36q^{51} + 24q^{53} + 112q^{57} + 92q^{63} - 76q^{65} - 16q^{67} + 80q^{71} + 36q^{73} - 252q^{75} + 48q^{77} - 4q^{79} - 16q^{85} - 60q^{87} - 192q^{89} + 112q^{91} + 16q^{93} + 48q^{95} - 208q^{99} + O(q^{100}) \)

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

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