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Properties

Label 1148.2.bz
Level $1148$
Weight $2$
Character orbit 1148.bz
Rep. character $\chi_{1148}(25,\cdot)$
Character field $\Q(\zeta_{30})$
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.bz (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 224 q - 4 q^{5} + 108 q^{9} + O(q^{10}) \) \( 224 q - 4 q^{5} + 108 q^{9} - 9 q^{21} + 3 q^{23} + 24 q^{25} - 40 q^{29} + 4 q^{31} - 5 q^{33} + 40 q^{35} - 5 q^{37} - 10 q^{39} + 10 q^{41} - 28 q^{43} + 22 q^{45} + 30 q^{47} - 36 q^{49} + 7 q^{51} + 25 q^{53} + 12 q^{57} + 26 q^{59} - 6 q^{61} + 40 q^{63} - 15 q^{65} - 20 q^{67} - 20 q^{69} + 10 q^{71} + 38 q^{73} - 5 q^{75} - 24 q^{77} - 152 q^{81} + 128 q^{83} + 2 q^{87} - 78 q^{91} - 20 q^{93} - 30 q^{95} - 40 q^{97} + 80 q^{99} + O(q^{100}) \)

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

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