Properties

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

Related objects

Downloads

Learn more about

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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1503, [\chi])\) into irreducible Hecke orbits

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

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