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Properties

Label 1575.4.ct
Level $1575$
Weight $4$
Character orbit 1575.ct
Rep. character $\chi_{1575}(106,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $4320$
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.ct (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 5792 4320 1472
Cusp forms 5728 4320 1408
Eisenstein series 64 0 64

Trace form

\( 4320 q - 8 q^{3} + 2160 q^{4} + 32 q^{5} + 64 q^{9} + O(q^{10}) \) \( 4320 q - 8 q^{3} + 2160 q^{4} + 32 q^{5} + 64 q^{9} - 176 q^{11} + 192 q^{12} - 112 q^{14} - 480 q^{15} + 8640 q^{16} + 936 q^{18} + 26 q^{20} + 360 q^{23} + 28 q^{24} - 576 q^{25} - 1184 q^{27} - 696 q^{29} - 200 q^{30} + 72 q^{31} + 460 q^{32} - 1112 q^{33} - 1718 q^{36} + 288 q^{37} - 3564 q^{38} - 732 q^{39} + 420 q^{42} + 3520 q^{44} + 2132 q^{45} - 2692 q^{47} + 1870 q^{48} - 105840 q^{49} + 1310 q^{50} - 520 q^{51} - 1360 q^{53} + 54 q^{54} + 792 q^{55} - 1344 q^{56} - 1432 q^{57} + 996 q^{59} - 7222 q^{60} - 6360 q^{62} - 1596 q^{63} - 69120 q^{64} - 1880 q^{65} - 7380 q^{66} + 1836 q^{67} + 1352 q^{68} + 3280 q^{69} + 5472 q^{71} + 6656 q^{72} + 7612 q^{74} + 4220 q^{75} + 3332 q^{78} + 12296 q^{80} + 728 q^{81} + 7488 q^{82} + 1880 q^{83} - 1656 q^{85} - 6220 q^{86} - 13708 q^{87} - 4176 q^{88} + 640 q^{89} + 3736 q^{90} - 2956 q^{92} - 10088 q^{93} + 4968 q^{94} + 3700 q^{95} - 5732 q^{96} - 3888 q^{97} - 824 q^{99} + O(q^{100}) \)

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

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