Properties

Label 1456.2.k
Level $1456$
Weight $2$
Character orbit 1456.k
Rep. character $\chi_{1456}(337,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $6$
Sturm bound $448$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(448\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1456, [\chi])\).

Total New Old
Modular forms 236 42 194
Cusp forms 212 42 170
Eisenstein series 24 0 24

Trace form

\( 42 q + 42 q^{9} + O(q^{10}) \) \( 42 q + 42 q^{9} + 2 q^{13} - 4 q^{17} - 12 q^{23} - 38 q^{25} + 24 q^{27} + 4 q^{29} - 12 q^{35} + 24 q^{39} + 28 q^{43} - 42 q^{49} - 4 q^{53} + 32 q^{55} - 20 q^{61} + 16 q^{75} + 44 q^{79} + 58 q^{81} - 72 q^{87} - 84 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1456, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1456.2.k.a 1456.k 13.b $2$ $11.626$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+2iq^{5}-iq^{7}-2q^{9}-5iq^{11}+\cdots\)
1456.2.k.b 1456.k 13.b $6$ $11.626$ 6.0.30647296.1 None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots\)
1456.2.k.c 1456.k 13.b $6$ $11.626$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+\beta _{3}q^{7}+\cdots\)
1456.2.k.d 1456.k 13.b $8$ $11.626$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{3}+\beta _{4})q^{5}+\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots\)
1456.2.k.e 1456.k 13.b $8$ $11.626$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{5})q^{5}+\beta _{5}q^{7}+\cdots\)
1456.2.k.f 1456.k 13.b $12$ $11.626$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{5}-\beta _{7})q^{5}-\beta _{4}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)