↑

Properties

Label 1575.4.ek
Level $1575$
Weight $4$
Character orbit 1575.ek
Rep. character $\chi_{1575}(2,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $11456$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.ek (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

\( 11456 q - 24 q^{2} - 8 q^{3} + 10 q^{4} - 24 q^{6} - 8 q^{7} - 10 q^{9} + O(q^{10}) \) \( 11456 q - 24 q^{2} - 8 q^{3} + 10 q^{4} - 24 q^{6} - 8 q^{7} - 10 q^{9} - 16 q^{10} + 132 q^{12} - 16 q^{13} - 30 q^{14} - 116 q^{15} - 22522 q^{16} - 144 q^{17} - 72 q^{18} - 20 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{22} - 16 q^{25} - 44 q^{27} - 144 q^{28} - 60 q^{29} - 1250 q^{30} + 6 q^{31} - 1020 q^{32} + 96 q^{33} - 20 q^{34} - 280 q^{36} - 16 q^{37} - 2450 q^{39} + 496 q^{40} - 36 q^{41} + 386 q^{42} - 16 q^{43} + 4248 q^{45} - 12 q^{46} - 24 q^{47} - 1898 q^{48} + 624 q^{50} - 16 q^{51} + 240 q^{52} - 10 q^{54} - 564 q^{55} - 18 q^{56} + 452 q^{57} - 1088 q^{58} - 30 q^{59} - 5256 q^{60} + 6 q^{61} - 1106 q^{63} - 80 q^{64} - 2112 q^{65} - 870 q^{66} + 8 q^{67} + 3040 q^{69} + 992 q^{70} - 828 q^{72} - 16 q^{73} - 12384 q^{75} + 224 q^{76} - 3240 q^{77} - 1234 q^{78} + 10 q^{79} - 1116 q^{80} - 6 q^{81} - 48 q^{83} - 3860 q^{84} - 16 q^{85} - 3594 q^{87} - 1616 q^{88} - 20400 q^{89} - 8476 q^{90} - 24 q^{91} - 3840 q^{92} + 1372 q^{93} + 10 q^{94} + 1476 q^{95} - 2502 q^{96} - 16 q^{97} + 192 q^{98} + O(q^{100}) \)

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.