Properties

Label 1248.2.m
Level $1248$
Weight $2$
Character orbit 1248.m
Rep. character $\chi_{1248}(337,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $3$
Sturm bound $448$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1248.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(448\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1248, [\chi])\).

Total New Old
Modular forms 240 28 212
Cusp forms 208 28 180
Eisenstein series 32 0 32

Trace form

\( 28 q - 28 q^{9} + O(q^{10}) \) \( 28 q - 28 q^{9} + 8 q^{17} + 36 q^{25} - 44 q^{49} - 48 q^{55} - 24 q^{65} + 40 q^{79} + 28 q^{81} - 24 q^{87} + 80 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1248, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1248.2.m.a 1248.m 104.e $2$ $9.965$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-2q^{5}-q^{9}+4q^{11}+(3-2i)q^{13}+\cdots\)
1248.2.m.b 1248.m 104.e $2$ $9.965$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{5}-q^{9}-4q^{11}+(-3+\cdots)q^{13}+\cdots\)
1248.2.m.c 1248.m 104.e $24$ $9.965$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1248, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)