Properties

Label 1503.2.c
Level $1503$
Weight $2$
Character orbit 1503.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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1503.2.c.a 1503.c 501.c $56$ $12.002$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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