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Properties

Label 1575.2.dl
Level $1575$
Weight $2$
Character orbit 1575.dl
Rep. character $\chi_{1575}(236,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1888$
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.dl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888 q - 9 q^{2} - 9 q^{3} - 229 q^{4} - 24 q^{5} + 12 q^{6} - 8 q^{7} - 3 q^{9} + O(q^{10}) \) \( 1888 q - 9 q^{2} - 9 q^{3} - 229 q^{4} - 24 q^{5} + 12 q^{6} - 8 q^{7} - 3 q^{9} - 24 q^{10} - 9 q^{12} - 9 q^{14} + 16 q^{15} + 231 q^{16} + 18 q^{17} + 16 q^{18} - 18 q^{19} + 6 q^{20} + 6 q^{21} - 14 q^{22} - 42 q^{24} - 8 q^{25} + 12 q^{26} - 36 q^{27} - 28 q^{28} - 18 q^{29} + 17 q^{30} - 9 q^{31} - 108 q^{32} - 54 q^{33} + 12 q^{34} - 75 q^{35} + 32 q^{36} - 6 q^{37} - 18 q^{38} - 13 q^{39} + 2 q^{42} - 16 q^{43} - 36 q^{44} - 3 q^{45} - 14 q^{46} - 9 q^{47} - 60 q^{48} - 8 q^{49} - 36 q^{50} - 8 q^{51} - 9 q^{54} + 54 q^{56} - 72 q^{57} - 14 q^{58} - 9 q^{59} - 31 q^{60} - 9 q^{61} + 132 q^{62} + 49 q^{63} + 420 q^{64} - 27 q^{65} + 3 q^{66} + 3 q^{67} - 624 q^{68} - 81 q^{69} + 72 q^{70} + 57 q^{72} - 18 q^{73} + 3 q^{75} - 57 q^{77} + 4 q^{78} - 9 q^{79} - 240 q^{80} - 7 q^{81} - 60 q^{82} - 3 q^{84} - 13 q^{85} + 9 q^{87} - 54 q^{88} - 45 q^{89} + 18 q^{90} - 54 q^{91} + 78 q^{92} + 26 q^{93} - 9 q^{94} - 42 q^{95} - 57 q^{96} - 18 q^{98} - 66 q^{99} + O(q^{100}) \)

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.