Properties

Label 2300.2.ba
Level $2300$
Weight $2$
Character orbit 2300.ba
Rep. character $\chi_{2300}(99,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2120$
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.ba (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 3720 2200 1520
Cusp forms 3480 2120 1360
Eisenstein series 240 80 160

Trace form

\( 2120q + 10q^{4} - 34q^{6} - 168q^{9} + O(q^{10}) \) \( 2120q + 10q^{4} - 34q^{6} - 168q^{9} + 22q^{14} - 26q^{16} - 44q^{21} + 44q^{24} + 10q^{26} + 20q^{29} + 66q^{34} - 46q^{36} - 52q^{41} - 44q^{44} + 22q^{46} + 240q^{49} + 210q^{54} - 22q^{56} - 44q^{61} - 26q^{64} - 88q^{66} + 52q^{69} + 22q^{74} - 132q^{76} - 16q^{81} + 22q^{84} - 242q^{86} + 44q^{89} - 10q^{94} - 300q^{96} + O(q^{100}) \)

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

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