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Properties

Label 1575.4.ei
Level $1575$
Weight $4$
Character orbit 1575.ei
Rep. character $\chi_{1575}(73,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $4768$
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.ei (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
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 11648 4832 6816
Cusp forms 11392 4768 6624
Eisenstein series 256 64 192

Trace form

\( 4768 q + 8 q^{2} - 10 q^{4} + 48 q^{5} + 84 q^{8} + O(q^{10}) \) \( 4768 q + 8 q^{2} - 10 q^{4} + 48 q^{5} + 84 q^{8} + 48 q^{10} + 6 q^{11} + 20 q^{14} - 9350 q^{16} - 120 q^{17} - 30 q^{19} + 752 q^{22} + 520 q^{23} + 176 q^{25} + 48 q^{26} - 350 q^{28} - 120 q^{29} - 18 q^{31} + 292 q^{32} - 184 q^{35} + 40 q^{37} + 5472 q^{38} - 2508 q^{40} + 888 q^{43} + 10 q^{44} - 6 q^{46} + 144 q^{47} + 7880 q^{50} - 8928 q^{52} - 1808 q^{53} - 244 q^{56} + 1024 q^{58} + 4950 q^{59} - 18 q^{61} - 9700 q^{64} + 292 q^{65} - 388 q^{67} + 4770 q^{68} - 1772 q^{70} + 24 q^{71} + 2424 q^{73} - 5878 q^{77} - 10 q^{79} + 5694 q^{80} - 1836 q^{82} + 1272 q^{85} + 6 q^{86} + 498 q^{88} - 20370 q^{89} - 12 q^{91} - 3764 q^{92} - 30 q^{94} + 3116 q^{95} - 14658 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)