Properties

Label 1575.2.cs
Level 1575
Weight 2
Character orbit cs
Rep. character \(\chi_{1575}(46,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 784
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.cs (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
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 1984 816 1168
Cusp forms 1856 784 1072
Eisenstein series 128 32 96

Trace form

\(784q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 14q^{7} \) \(\mathstrut +\mathstrut 38q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(784q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 14q^{7} \) \(\mathstrut +\mathstrut 38q^{8} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 93q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 32q^{20} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 5q^{23} \) \(\mathstrut -\mathstrut 7q^{25} \) \(\mathstrut -\mathstrut 44q^{26} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 9q^{31} \) \(\mathstrut +\mathstrut 40q^{32} \) \(\mathstrut +\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 11q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 36q^{43} \) \(\mathstrut +\mathstrut 23q^{44} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 82q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 23q^{53} \) \(\mathstrut -\mathstrut 52q^{55} \) \(\mathstrut +\mathstrut 60q^{56} \) \(\mathstrut -\mathstrut 59q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 13q^{61} \) \(\mathstrut +\mathstrut 92q^{62} \) \(\mathstrut -\mathstrut 214q^{64} \) \(\mathstrut -\mathstrut q^{65} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut +\mathstrut 122q^{68} \) \(\mathstrut -\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 47q^{73} \) \(\mathstrut +\mathstrut 22q^{74} \) \(\mathstrut -\mathstrut 228q^{76} \) \(\mathstrut -\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut q^{79} \) \(\mathstrut +\mathstrut 70q^{80} \) \(\mathstrut +\mathstrut 28q^{82} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut -\mathstrut 98q^{85} \) \(\mathstrut +\mathstrut 41q^{86} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 38q^{91} \) \(\mathstrut +\mathstrut 154q^{92} \) \(\mathstrut -\mathstrut 43q^{94} \) \(\mathstrut +\mathstrut 57q^{95} \) \(\mathstrut -\mathstrut 168q^{97} \) \(\mathstrut -\mathstrut 106q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)