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Properties

Label 1500.4.e
Level $1500$
Weight $4$
Character orbit 1500.e
Rep. character $\chi_{1500}(251,\cdot)$
Character field $\Q$
Dimension $576$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1500.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1500, [\chi])\).

Total New Old
Modular forms 920 576 344
Cusp forms 880 576 304
Eisenstein series 40 0 40

Trace form

\( 576 q - 6 q^{4} + O(q^{10}) \) \( 576 q - 6 q^{4} - 66 q^{16} + 68 q^{21} + 184 q^{24} + 288 q^{34} + 104 q^{36} - 204 q^{46} - 28224 q^{49} - 206 q^{54} - 912 q^{61} + 42 q^{64} + 1062 q^{66} + 508 q^{69} + 1200 q^{76} - 1540 q^{81} + 976 q^{84} - 4254 q^{94} - 324 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1500, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1500, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1500, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)