Properties

Label 1248.1.l
Level $1248$
Weight $1$
Character orbit 1248.l
Rep. character $\chi_{1248}(545,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1248.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1248, [\chi])\).

Total New Old
Modular forms 28 4 24
Cusp forms 12 4 8
Eisenstein series 16 0 16

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{9} - 4 q^{13} + 4 q^{25} - 4 q^{49} + 8 q^{69} + 4 q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1248, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1248.1.l.a 1248.l 39.d $4$ $0.623$ \(\Q(\zeta_{8})\) $D_{4}$ None \(\Q(\sqrt{39}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1248, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1248, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)