Properties

Label 1575.2.eg
Level 1575
Weight 2
Character orbit eg
Rep. character \(\chi_{1575}(13,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 3776
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.eg (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 3904 3904 0
Cusp forms 3776 3776 0
Eisenstein series 128 128 0

Trace form

\( 3776q - 16q^{2} - 20q^{4} - 8q^{7} - 48q^{8} - 40q^{9} + O(q^{10}) \) \( 3776q - 16q^{2} - 20q^{4} - 8q^{7} - 48q^{8} - 40q^{9} - 12q^{11} - 10q^{14} - 20q^{15} - 460q^{16} - 32q^{18} - 12q^{21} - 32q^{22} - 8q^{23} - 16q^{25} - 8q^{28} - 20q^{29} + 16q^{30} - 68q^{32} - 32q^{35} + 8q^{36} - 64q^{37} - 58q^{42} - 16q^{43} - 80q^{44} - 48q^{46} + 56q^{50} - 64q^{51} - 144q^{53} + 26q^{56} - 88q^{57} + 24q^{58} - 200q^{60} - 94q^{63} - 80q^{64} - 40q^{65} - 16q^{67} - 28q^{70} - 48q^{71} - 20q^{72} + 44q^{77} + 4q^{78} - 20q^{79} - 24q^{81} - 140q^{84} - 16q^{85} - 12q^{86} + 40q^{88} - 24q^{91} + 48q^{92} - 128q^{93} - 60q^{95} + 40q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database