Properties

Label 1575.4.ef
Level $1575$
Weight $4$
Character orbit 1575.ef
Rep. character $\chi_{1575}(92,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $8640$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.ef (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1575, [\chi])\).

Total New Old
Modular forms 11584 8640 2944
Cusp forms 11456 8640 2816
Eisenstein series 128 0 128

Trace form

\( 8640 q + 8 q^{3} + O(q^{10}) \) \( 8640 q + 8 q^{3} - 128 q^{12} - 16 q^{15} - 17280 q^{16} - 968 q^{18} + 768 q^{20} + 312 q^{23} + 1152 q^{25} + 1184 q^{27} - 580 q^{30} - 1380 q^{32} - 1112 q^{33} + 288 q^{37} + 144 q^{38} + 2440 q^{39} - 1120 q^{42} + 1760 q^{45} + 6936 q^{47} - 5172 q^{48} - 7540 q^{54} + 1584 q^{55} - 1112 q^{57} - 9960 q^{59} - 20948 q^{60} + 4256 q^{63} - 2088 q^{65} + 1224 q^{67} + 18168 q^{72} - 4632 q^{75} + 5464 q^{78} - 1280 q^{81} - 7488 q^{82} + 5640 q^{83} - 3312 q^{85} + 1368 q^{87} - 4176 q^{88} + 14628 q^{90} + 22668 q^{92} + 1512 q^{93} - 16560 q^{94} + 7080 q^{95} + 720 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)