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Properties

Label 1148.2.br
Level $1148$
Weight $2$
Character orbit 1148.br
Rep. character $\chi_{1148}(325,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $224$
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.br (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 1392 224 1168
Cusp forms 1296 224 1072
Eisenstein series 96 0 96

Trace form

\( 224 q - 8 q^{9} + O(q^{10}) \) \( 224 q - 8 q^{9} + 24 q^{15} + 36 q^{17} - 24 q^{19} - 8 q^{21} + 32 q^{29} + 60 q^{33} + 24 q^{37} + 16 q^{43} + 24 q^{47} + 48 q^{49} + 24 q^{51} - 24 q^{53} - 112 q^{57} - 92 q^{63} + 76 q^{65} + 16 q^{67} - 80 q^{71} - 36 q^{73} - 228 q^{75} + 32 q^{77} + 4 q^{79} + 16 q^{85} + 60 q^{87} - 48 q^{89} + 48 q^{91} - 16 q^{93} - 48 q^{95} + 208 q^{99} + O(q^{100}) \)

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

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