Properties

Label 2300.2.e
Level $2300$
Weight $2$
Character orbit 2300.e
Rep. character $\chi_{2300}(551,\cdot)$
Character field $\Q$
Dimension $222$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2300.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2300, [\chi])\).

Total New Old
Modular forms 372 234 138
Cusp forms 348 222 126
Eisenstein series 24 12 12

Trace form

\( 222q - 4q^{4} - 3q^{6} + 3q^{8} - 206q^{9} + O(q^{10}) \) \( 222q - 4q^{4} - 3q^{6} + 3q^{8} - 206q^{9} - q^{12} + 4q^{13} - 12q^{16} + 13q^{18} + 16q^{24} + q^{26} + 12q^{29} - 33q^{36} - 4q^{41} - 53q^{48} + 198q^{49} - 53q^{52} - 7q^{54} + 9q^{58} + 5q^{62} - 61q^{64} + 52q^{69} + 67q^{72} + 4q^{73} + 56q^{77} - 99q^{78} + 94q^{81} - 23q^{82} - 40q^{92} + 72q^{93} - 7q^{94} - 5q^{96} - 16q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2300, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)