Properties

Label 1503.2.c
Level 1503
Weight 2
Character orbit c
Rep. character \(\chi_{1503}(1502,\cdot)\)
Character field \(\Q\)
Dimension 56
Newform subspaces 1
Sturm bound 336
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 1503 = 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1503.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 501 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(336\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1503, [\chi])\).

Total New Old
Modular forms 172 56 116
Cusp forms 164 56 108
Eisenstein series 8 0 8

Trace form

\( 56q - 48q^{4} + O(q^{10}) \) \( 56q - 48q^{4} + 32q^{16} - 8q^{19} + 16q^{22} + 64q^{25} - 32q^{28} + 40q^{31} + 56q^{49} - 32q^{58} + 24q^{61} - 56q^{76} + 72q^{88} - 56q^{94} - 48q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1503, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1503.2.c.a \(56\) \(12.002\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1503, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1503, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(501, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database