Properties

Label 3150.2.em
Level 3150
Weight 2
Character orbit em
Rep. character \(\chi_{3150}(73,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 1600
Sturm bound 1440

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Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.em (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 11776 1600 10176
Cusp forms 11264 1600 9664
Eisenstein series 512 0 512

Trace form

\( 1600q + 12q^{5} + O(q^{10}) \) \( 1600q + 12q^{5} - 12q^{10} - 200q^{16} - 36q^{17} + 72q^{22} + 28q^{23} + 4q^{25} + 8q^{28} - 80q^{29} - 52q^{35} - 20q^{37} - 24q^{38} + 56q^{43} - 12q^{47} - 32q^{50} - 92q^{53} + 24q^{58} - 120q^{59} + 24q^{65} + 144q^{68} - 44q^{70} + 60q^{73} - 144q^{77} + 12q^{80} + 192q^{82} + 104q^{85} - 4q^{88} + 300q^{89} + 24q^{92} + 84q^{95} + 56q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database