Properties

Label 2300.2.bi
Level $2300$
Weight $2$
Character orbit 2300.bi
Rep. character $\chi_{2300}(243,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $4240$
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.bi (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 7440 4400 3040
Cusp forms 6960 4240 2720
Eisenstein series 480 160 320

Trace form

\( 4240q + 18q^{2} - 20q^{6} + 18q^{8} + O(q^{10}) \) \( 4240q + 18q^{2} - 20q^{6} + 18q^{8} + 6q^{12} + 36q^{13} - 20q^{16} + 36q^{17} + 38q^{18} - 40q^{21} + 28q^{22} - 36q^{26} + 34q^{28} - 2q^{32} + 60q^{33} - 132q^{36} + 36q^{37} + 10q^{38} - 104q^{41} + 202q^{42} - 92q^{46} + 50q^{48} + 250q^{52} + 84q^{53} - 60q^{56} + 44q^{57} + 58q^{58} + 56q^{61} + 82q^{62} - 84q^{66} + 4q^{68} + 104q^{72} + 36q^{73} - 20q^{76} + 44q^{77} + 50q^{78} + 128q^{81} + 10q^{82} - 76q^{86} + 50q^{88} + 22q^{92} + 88q^{93} + 28q^{96} + 36q^{97} - 30q^{98} + O(q^{100}) \)

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

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