Properties

Label 1575.2.ei
Level 1575
Weight 2
Character orbit ei
Rep. character \(\chi_{1575}(73,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 1568
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.ei (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
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 3968 1632 2336
Cusp forms 3712 1568 2144
Eisenstein series 256 64 192

Trace form

\( 1568q + 8q^{2} - 10q^{4} + 18q^{5} - 18q^{7} + 12q^{8} + O(q^{10}) \) \( 1568q + 8q^{2} - 10q^{4} + 18q^{5} - 18q^{7} + 12q^{8} - 12q^{10} + 6q^{11} + 20q^{14} - 190q^{16} + 42q^{17} - 30q^{19} - 112q^{22} - 8q^{23} - 14q^{25} + 48q^{26} - 10q^{28} + 80q^{29} - 18q^{31} + 16q^{32} + 66q^{35} + 6q^{37} + 120q^{38} + 72q^{40} - 92q^{43} + 10q^{44} - 6q^{46} - 6q^{47} - 40q^{50} + 216q^{52} + 86q^{53} - 4q^{56} - 76q^{58} + 150q^{59} - 18q^{61} - 100q^{64} - 18q^{65} - 28q^{67} - 210q^{68} + 68q^{70} + 24q^{71} - 78q^{73} + 140q^{77} - 10q^{79} - 6q^{80} - 288q^{82} - 128q^{85} + 6q^{86} + 94q^{88} - 120q^{89} - 12q^{91} - 52q^{92} - 30q^{94} - 74q^{95} + 266q^{98} + O(q^{100}) \)

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

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

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database