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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

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

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

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