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Properties

Label 1575.4.ep
Level $1575$
Weight $4$
Character orbit 1575.ep
Rep. character $\chi_{1575}(52,\cdot)$
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.ep (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

\( 11456 q - 16 q^{2} - 24 q^{3} - 20 q^{4} - 24 q^{5} - 8 q^{7} - 96 q^{8} - 10 q^{9} + O(q^{10}) \) \( 11456 q - 16 q^{2} - 24 q^{3} - 20 q^{4} - 24 q^{5} - 8 q^{7} - 96 q^{8} - 10 q^{9} - 48 q^{10} + 6 q^{11} + 24 q^{12} - 10 q^{14} + 52 q^{15} + 45044 q^{16} - 192 q^{17} - 56 q^{18} - 60 q^{19} - 768 q^{20} - 12 q^{21} + 16 q^{22} + 112 q^{23} + 8 q^{25} - 96 q^{26} - 828 q^{27} - 176 q^{28} - 20 q^{29} + 904 q^{30} - 1064 q^{32} - 24 q^{33} + 544 q^{35} - 280 q^{36} - 16 q^{37} - 24 q^{38} - 4890 q^{39} - 24 q^{40} - 316 q^{42} - 16 q^{43} - 20 q^{44} + 5544 q^{45} - 12 q^{46} - 30 q^{48} + 1448 q^{50} - 16 q^{51} - 792 q^{52} - 576 q^{53} - 30 q^{54} - 1030 q^{56} - 2308 q^{57} + 480 q^{58} + 6424 q^{60} - 4228 q^{63} - 80 q^{64} - 1408 q^{65} - 18 q^{66} - 16 q^{67} - 9336 q^{68} - 9240 q^{69} - 508 q^{70} - 48 q^{71} - 5216 q^{72} - 48 q^{73} + 14184 q^{75} - 768 q^{76} - 7876 q^{77} - 5390 q^{78} - 20 q^{79} - 432 q^{80} - 6 q^{81} + 672 q^{83} - 1940 q^{84} - 16 q^{85} + 6 q^{86} - 3660 q^{87} - 1304 q^{88} - 20460 q^{89} + 23904 q^{90} - 24 q^{91} + 960 q^{92} - 632 q^{93} - 120 q^{95} + 2574 q^{96} + 4300 q^{98} + O(q^{100}) \)

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.