Properties

Label 1575.2.bx
Level 1575
Weight 2
Character orbit bx
Rep. character \(\chi_{1575}(64,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 296
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.bx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 992 296 696
Cusp forms 928 296 632
Eisenstein series 64 0 64

Trace form

\(296q \) \(\mathstrut +\mathstrut 72q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(296q \) \(\mathstrut +\mathstrut 72q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 44q^{16} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 70q^{22} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 40q^{25} \) \(\mathstrut +\mathstrut 12q^{26} \) \(\mathstrut +\mathstrut 22q^{29} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut 12q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut +\mathstrut 70q^{38} \) \(\mathstrut +\mathstrut 126q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 62q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut +\mathstrut 90q^{47} \) \(\mathstrut -\mathstrut 296q^{49} \) \(\mathstrut -\mathstrut 94q^{50} \) \(\mathstrut -\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 12q^{56} \) \(\mathstrut +\mathstrut 130q^{58} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 20q^{61} \) \(\mathstrut +\mathstrut 50q^{62} \) \(\mathstrut +\mathstrut 36q^{64} \) \(\mathstrut -\mathstrut 98q^{65} \) \(\mathstrut -\mathstrut 70q^{67} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 40q^{73} \) \(\mathstrut -\mathstrut 44q^{74} \) \(\mathstrut -\mathstrut 12q^{76} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 48q^{79} \) \(\mathstrut -\mathstrut 80q^{80} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 52q^{85} \) \(\mathstrut -\mathstrut 100q^{86} \) \(\mathstrut -\mathstrut 140q^{88} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 120q^{92} \) \(\mathstrut -\mathstrut 54q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)