Properties

Label 1575.2.cf
Level 1575
Weight 2
Character orbit cf
Rep. character \(\chi_{1575}(32,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 560
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.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

Trace form

\(560q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(560q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 22q^{12} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 260q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut -\mathstrut 64q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 90q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 32q^{46} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 38q^{48} \) \(\mathstrut -\mathstrut 52q^{51} \) \(\mathstrut +\mathstrut 52q^{52} \) \(\mathstrut +\mathstrut 156q^{56} \) \(\mathstrut -\mathstrut 32q^{57} \) \(\mathstrut +\mathstrut 12q^{58} \) \(\mathstrut +\mathstrut 28q^{61} \) \(\mathstrut -\mathstrut 14q^{63} \) \(\mathstrut +\mathstrut 244q^{66} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 46q^{72} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 24q^{76} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut -\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 8q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 72q^{92} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 36q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 12q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)