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Properties

Label 1575.4.eb
Level $1575$
Weight $4$
Character orbit 1575.eb
Rep. character $\chi_{1575}(187,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $11456$
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.eb (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
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 11584 0
Cusp forms 11456 11456 0
Eisenstein series 128 128 0

Trace form

\( 11456 q + 8 q^{2} - 24 q^{3} + 10 q^{4} - 8 q^{7} - 96 q^{8} - 10 q^{9} + O(q^{10}) \) \( 11456 q + 8 q^{2} - 24 q^{3} + 10 q^{4} - 8 q^{7} - 96 q^{8} - 10 q^{9} - 48 q^{10} - 12 q^{11} - 24 q^{12} - 10 q^{14} + 52 q^{15} - 22522 q^{16} - 192 q^{17} - 8 q^{18} - 60 q^{19} + 768 q^{20} - 12 q^{21} + 16 q^{22} - 224 q^{23} - 16 q^{25} - 96 q^{26} + 828 q^{27} - 176 q^{28} - 20 q^{29} - 1586 q^{30} - 18 q^{31} + 532 q^{32} + 936 q^{33} + 544 q^{35} - 280 q^{36} - 16 q^{37} + 2430 q^{39} - 526 q^{42} - 16 q^{43} - 20 q^{44} - 1392 q^{45} - 12 q^{46} - 24 q^{47} + 30 q^{48} + 1448 q^{50} - 16 q^{51} - 576 q^{53} - 30 q^{54} + 506 q^{56} - 2308 q^{57} - 960 q^{58} - 30 q^{59} + 3640 q^{60} - 18 q^{61} + 8174 q^{63} - 80 q^{64} + 704 q^{65} + 2574 q^{66} + 8 q^{67} + 9240 q^{69} + 992 q^{70} - 48 q^{71} + 1324 q^{72} - 48 q^{73} - 24 q^{75} + 768 q^{76} + 12512 q^{77} - 5390 q^{78} + 10 q^{79} - 432 q^{80} - 6 q^{81} - 672 q^{83} + 3820 q^{84} - 16 q^{85} - 12 q^{86} + 138 q^{87} + 2608 q^{88} - 20460 q^{89} - 23904 q^{90} - 24 q^{91} + 960 q^{92} + 5284 q^{93} - 30 q^{94} + 60 q^{95} - 18 q^{96} + 4300 q^{98} + O(q^{100}) \)

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.