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Properties

Label 1456.2.cc
Level $1456$
Weight $2$
Character orbit 1456.cc
Rep. character $\chi_{1456}(225,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $84$
Newform subspaces $7$
Sturm bound $448$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.cc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(448\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 472 84 388
Cusp forms 424 84 340
Eisenstein series 48 0 48

Trace form

\( 84 q - 42 q^{9} + O(q^{10}) \) \( 84 q - 42 q^{9} - 2 q^{13} - 2 q^{17} + 12 q^{23} - 88 q^{25} - 24 q^{27} + 2 q^{29} + 12 q^{35} + 30 q^{37} + 12 q^{39} + 6 q^{41} - 28 q^{43} - 30 q^{45} + 42 q^{49} + 72 q^{51} + 4 q^{53} + 40 q^{55} + 36 q^{59} - 10 q^{61} + 6 q^{65} - 72 q^{67} - 36 q^{71} - 16 q^{75} + 16 q^{79} - 34 q^{81} - 6 q^{85} - 36 q^{87} + 24 q^{89} + 24 q^{95} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.cc.a 1456.cc 13.e $4$ $11.626$ \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+2\zeta_{12}^{2})q^{3}+(1-2\zeta_{12}^{2})q^{5}+\cdots\)
1456.2.cc.b 1456.cc 13.e $4$ $11.626$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)
1456.2.cc.c 1456.cc 13.e $12$ $11.626$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{10})q^{3}+(-\beta _{3}-\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots\)
1456.2.cc.d 1456.cc 13.e $12$ $11.626$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{10}q^{3}+(-\beta _{1}+\beta _{5}-\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots\)
1456.2.cc.e 1456.cc 13.e $12$ $11.626$ 12.0.\(\cdots\).1 None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}+\beta _{8})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{6}+\cdots)q^{5}+\cdots\)
1456.2.cc.f 1456.cc 13.e $16$ $11.626$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{2}-\beta _{14})q^{3}+(\beta _{2}+\beta _{12}+\cdots)q^{5}+\cdots\)
1456.2.cc.g 1456.cc 13.e $24$ $11.626$ None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)