Properties

Label 1560.2.ec
Level $1560$
Weight $2$
Character orbit 1560.ec
Rep. character $\chi_{1560}(121,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $5$
Sturm bound $672$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.ec (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(672\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).

Total New Old
Modular forms 704 56 648
Cusp forms 640 56 584
Eisenstein series 64 0 64

Trace form

\( 56 q + 4 q^{3} - 12 q^{7} - 28 q^{9} + O(q^{10}) \) \( 56 q + 4 q^{3} - 12 q^{7} - 28 q^{9} + 12 q^{11} + 4 q^{13} - 8 q^{17} - 12 q^{19} - 8 q^{23} - 56 q^{25} - 8 q^{27} + 8 q^{29} - 4 q^{35} + 4 q^{39} - 12 q^{43} + 12 q^{49} + 16 q^{51} + 48 q^{53} + 4 q^{55} + 72 q^{59} - 28 q^{61} + 12 q^{63} - 12 q^{65} - 12 q^{67} + 24 q^{71} - 4 q^{75} - 32 q^{77} - 48 q^{79} - 28 q^{81} + 8 q^{87} - 36 q^{89} - 40 q^{91} - 12 q^{93} + 60 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1560.2.ec.a 1560.ec 13.e $8$ $12.457$ \(\Q(\zeta_{24})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{4}q^{3}-\zeta_{24}^{6}q^{5}+(\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
1560.2.ec.b 1560.ec 13.e $8$ $12.457$ 8.0.56070144.2 None \(0\) \(4\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{6})q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1560.2.ec.c 1560.ec 13.e $8$ $12.457$ 8.0.\(\cdots\).1 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2})q^{3}+\beta _{4}q^{5}+(\beta _{3}+\beta _{4})q^{7}+\cdots\)
1560.2.ec.d 1560.ec 13.e $16$ $12.457$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{5})q^{3}+\beta _{12}q^{5}+(\beta _{1}-\beta _{9}+\cdots)q^{7}+\cdots\)
1560.2.ec.e 1560.ec 13.e $16$ $12.457$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(8\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{7}q^{3}+(-\beta _{8}+\beta _{9})q^{5}+(-\beta _{11}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)