Properties

Label 1575.2.cr
Level 1575
Weight 2
Character orbit 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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into irreducible Hecke orbits

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