Properties

Label 1575.2.de
Level 1575
Weight 2
Character orbit de
Rep. character \(\chi_{1575}(41,\cdot)\)
Character field \(\Q(\zeta_{30})\)
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.de (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 1888q - 18q^{2} - 238q^{4} - 8q^{7} - 12q^{9} + O(q^{10}) \) \( 1888q - 18q^{2} - 238q^{4} - 8q^{7} - 12q^{9} - 18q^{11} - 9q^{14} + 16q^{15} + 210q^{16} - 32q^{18} - 3q^{21} + 10q^{22} - 42q^{23} - 8q^{25} + 20q^{28} - 18q^{29} - 64q^{30} - 36q^{32} - 10q^{36} - 24q^{37} - 52q^{39} - 46q^{42} - 16q^{43} - 8q^{46} - 8q^{49} + 36q^{50} - 32q^{51} + 66q^{56} + 120q^{57} - 14q^{58} + 56q^{60} + 4q^{63} + 336q^{64} + 54q^{65} - 6q^{67} + 36q^{70} - 72q^{72} - 24q^{74} - 33q^{77} + 76q^{78} + 18q^{79} + 92q^{81} - 15q^{84} + 2q^{85} + 42q^{86} - 78q^{88} - 54q^{91} + 114q^{92} - 160q^{93} - 102q^{95} - 12q^{99} + O(q^{100}) \)

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