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Properties

Label 1575.2.cr
Level $1575$
Weight $2$
Character orbit 1575.cr
Rep. character $\chi_{1575}(16,\cdot)$
Character field $\Q(\zeta_{15})$
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.cr (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 1888 q + 3 q^{2} - 3 q^{3} + 235 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 16 q^{8} - 3 q^{9} + O(q^{10}) \) \( 1888 q + 3 q^{2} - 3 q^{3} + 235 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 16 q^{8} - 3 q^{9} - 4 q^{10} - 6 q^{11} - 23 q^{12} - 6 q^{13} + 9 q^{14} - 42 q^{15} + 223 q^{16} - 12 q^{17} - 6 q^{19} - 2 q^{20} - 30 q^{21} + 2 q^{22} - 22 q^{23} - 26 q^{24} - 8 q^{25} + 76 q^{26} + 18 q^{27} - 20 q^{28} - 6 q^{29} + 25 q^{30} + 3 q^{31} + 4 q^{32} + 6 q^{33} - 10 q^{34} - 49 q^{35} + 20 q^{36} - 6 q^{37} - 22 q^{38} + 7 q^{39} - 22 q^{40} - 38 q^{41} - 26 q^{42} - 16 q^{43} + 6 q^{44} + 73 q^{45} + 2 q^{46} + 3 q^{47} + 44 q^{48} - 8 q^{49} - 28 q^{50} - 8 q^{51} - 14 q^{52} + 14 q^{53} - 11 q^{54} - 34 q^{55} - 48 q^{56} - 144 q^{57} - 46 q^{58} - 45 q^{59} + 53 q^{60} + 3 q^{61} - 52 q^{62} - 11 q^{63} - 436 q^{64} + 19 q^{65} + 5 q^{66} + 3 q^{67} - 256 q^{68} - 27 q^{69} + 8 q^{70} - 42 q^{71} - 15 q^{72} - 6 q^{73} - 32 q^{74} + 97 q^{75} - 16 q^{76} - 23 q^{77} + 40 q^{78} + 15 q^{79} + 94 q^{80} + q^{81} - 20 q^{82} - 48 q^{83} - 125 q^{84} - 13 q^{85} - 22 q^{86} - 41 q^{87} - 22 q^{88} - 39 q^{89} - 178 q^{90} + 30 q^{91} - 30 q^{92} + 50 q^{93} - 13 q^{94} + 18 q^{95} + 23 q^{96} - 6 q^{97} - 142 q^{98} - 30 q^{99} + O(q^{100}) \)

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.