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Properties

Label 1575.4.l
Level $1575$
Weight $4$
Character orbit 1575.l
Rep. character $\chi_{1575}(151,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $900$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1464 924 540
Cusp forms 1416 900 516
Eisenstein series 48 24 24

Trace form

\( 900 q + 2 q^{2} + q^{3} + 3554 q^{4} + 4 q^{6} - 5 q^{7} + 24 q^{8} - 11 q^{9} + O(q^{10}) \) \( 900 q + 2 q^{2} + q^{3} + 3554 q^{4} + 4 q^{6} - 5 q^{7} + 24 q^{8} - 11 q^{9} - q^{11} + 172 q^{12} - 10 q^{13} - 26 q^{14} + 13834 q^{16} - 110 q^{17} - 106 q^{18} + 62 q^{19} - 109 q^{21} + 18 q^{22} + 9 q^{23} + 234 q^{24} + 338 q^{26} - 260 q^{27} - 20 q^{28} - 248 q^{29} - 126 q^{31} + 1634 q^{32} + 611 q^{33} + 26 q^{34} - 866 q^{36} - 82 q^{37} - 731 q^{38} + 568 q^{39} + 204 q^{41} - 308 q^{42} - 82 q^{43} - 295 q^{44} + 262 q^{46} + 2014 q^{47} + 921 q^{48} - 77 q^{49} - 133 q^{51} - 49 q^{52} + 822 q^{53} + 1351 q^{54} + 2124 q^{56} + 506 q^{57} - 237 q^{58} - 2330 q^{59} - 810 q^{61} + 3828 q^{62} - 324 q^{63} + 52312 q^{64} + 2174 q^{66} - 586 q^{67} - 320 q^{68} - 3817 q^{69} + 132 q^{71} - 344 q^{72} - 334 q^{73} + 1477 q^{74} + 1162 q^{76} - 2333 q^{77} - 869 q^{78} + 1106 q^{79} + 1621 q^{81} - 6 q^{82} - 1408 q^{83} - 777 q^{84} + 4147 q^{86} - 3433 q^{87} - 369 q^{88} + 2200 q^{89} + 172 q^{91} + 1096 q^{92} - 1071 q^{93} - 2638 q^{94} + 1589 q^{96} - 262 q^{97} + 7893 q^{98} - 25 q^{99} + O(q^{100}) \)

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

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