Properties

Label 1512.2.p
Level 1512
Weight 2
Character orbit p
Rep. character \(\chi_{1512}(811,\cdot)\)
Character field \(\Q\)
Dimension 128
Sturm bound 576

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Defining parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 56 \)
Character field: \(\Q\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 300 128 172
Cusp forms 276 128 148
Eisenstein series 24 0 24

Trace form

\( 128q + O(q^{10}) \) \( 128q + 16q^{16} - 28q^{22} + 128q^{25} + 14q^{28} - 36q^{46} + 8q^{49} + 20q^{58} + 24q^{64} + 64q^{67} - 18q^{70} - 4q^{88} + 24q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database