↑

Properties

Label 1575.2.ek
Level $1575$
Weight $2$
Character orbit 1575.ek
Rep. character $\chi_{1575}(2,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3776$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.ek (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 3904 3904 0
Cusp forms 3776 3776 0
Eisenstein series 128 128 0

Trace form

\( 3776 q - 24 q^{2} - 8 q^{3} + 10 q^{4} - 24 q^{6} - 8 q^{7} - 10 q^{9} + O(q^{10}) \) \( 3776 q - 24 q^{2} - 8 q^{3} + 10 q^{4} - 24 q^{6} - 8 q^{7} - 10 q^{9} - 16 q^{10} + 12 q^{12} - 16 q^{13} - 30 q^{14} - 26 q^{15} - 442 q^{16} + 18 q^{17} - 20 q^{19} - 48 q^{20} - 12 q^{21} - 24 q^{22} - 16 q^{25} - 8 q^{27} - 36 q^{28} - 60 q^{29} + 10 q^{30} + 6 q^{31} + 60 q^{32} - 42 q^{33} - 20 q^{34} - 40 q^{36} - 16 q^{37} - 50 q^{39} + 16 q^{40} - 36 q^{41} - 34 q^{42} - 16 q^{43} - 102 q^{45} - 12 q^{46} - 24 q^{47} - 98 q^{48} - 96 q^{50} - 16 q^{51} - 48 q^{52} - 10 q^{54} - 84 q^{55} - 18 q^{56} + 8 q^{57} - 8 q^{58} - 30 q^{59} - 36 q^{60} + 6 q^{61} - 134 q^{63} - 80 q^{64} + 48 q^{65} - 30 q^{66} + 8 q^{67} - 110 q^{69} + 32 q^{70} + 36 q^{72} - 16 q^{73} + 96 q^{75} - 16 q^{76} - 72 q^{77} - 154 q^{78} + 10 q^{79} - 36 q^{80} - 6 q^{81} - 12 q^{82} - 48 q^{83} - 260 q^{84} - 16 q^{85} + 18 q^{87} - 32 q^{88} - 150 q^{89} - 76 q^{90} - 24 q^{91} - 132 q^{92} - 14 q^{93} + 10 q^{94} + 36 q^{95} - 102 q^{96} - 16 q^{97} + 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.