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

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

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

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