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Properties

Label 1575.2.em
Level $1575$
Weight $2$
Character orbit 1575.em
Rep. character $\chi_{1575}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3776$
Sturm bound $480$

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Defining parameters

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

\( 3776 q - 8 q^{3} - 20 q^{4} - 24 q^{5} - 24 q^{6} - 8 q^{7} - 10 q^{9} + O(q^{10}) \) \( 3776 q - 8 q^{3} - 20 q^{4} - 24 q^{5} - 24 q^{6} - 8 q^{7} - 10 q^{9} - 16 q^{10} - 18 q^{11} - 36 q^{12} - 16 q^{13} - 30 q^{14} - 26 q^{15} + 884 q^{16} - 18 q^{17} - 20 q^{19} - 48 q^{20} - 12 q^{21} - 24 q^{22} + 8 q^{25} - 8 q^{27} - 36 q^{28} - 60 q^{29} - 20 q^{30} - 12 q^{31} + 24 q^{33} - 20 q^{34} - 40 q^{36} - 16 q^{37} + 70 q^{39} - 8 q^{40} - 36 q^{41} - 28 q^{42} - 16 q^{43} + 48 q^{45} - 12 q^{46} - 98 q^{48} - 96 q^{50} - 16 q^{51} + 24 q^{52} - 10 q^{54} - 84 q^{55} - 18 q^{56} + 8 q^{57} + 4 q^{58} - 132 q^{60} - 12 q^{61} + 16 q^{63} - 80 q^{64} + 42 q^{66} - 16 q^{67} + 216 q^{68} - 110 q^{69} - 28 q^{70} + 36 q^{72} - 16 q^{73} - 96 q^{75} - 16 q^{76} - 216 q^{77} - 154 q^{78} - 20 q^{79} + 36 q^{80} - 6 q^{81} - 12 q^{82} - 48 q^{83} + 100 q^{84} - 16 q^{85} - 18 q^{86} + 18 q^{87} + 16 q^{88} + 150 q^{89} - 76 q^{90} - 24 q^{91} - 132 q^{92} + 28 q^{93} - 20 q^{94} + 114 q^{96} - 16 q^{97} - 48 q^{98} + O(q^{100}) \)

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.