Properties

Label 1320.2.w
Level $1320$
Weight $2$
Character orbit 1320.w
Rep. character $\chi_{1320}(661,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $6$
Sturm bound $576$
Trace bound $22$

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Defining parameters

Level: \( N \) \(=\) \( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1320.w (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(576\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(7\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1320, [\chi])\).

Total New Old
Modular forms 296 80 216
Cusp forms 280 80 200
Eisenstein series 16 0 16

Trace form

\( 80 q - 4 q^{4} - 4 q^{6} - 80 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{4} - 4 q^{6} - 80 q^{9} + 4 q^{10} + 8 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{20} + 4 q^{24} - 80 q^{25} - 48 q^{26} + 40 q^{28} - 16 q^{31} - 40 q^{32} - 8 q^{34} + 4 q^{36} + 40 q^{38} - 4 q^{40} + 8 q^{44} + 40 q^{46} + 48 q^{49} + 4 q^{54} - 16 q^{55} + 8 q^{56} + 32 q^{57} + 56 q^{58} - 4 q^{60} - 8 q^{62} - 52 q^{64} + 32 q^{68} + 8 q^{70} + 32 q^{71} + 32 q^{73} - 80 q^{74} - 24 q^{76} + 16 q^{79} - 32 q^{80} + 80 q^{81} - 88 q^{82} - 16 q^{86} - 4 q^{90} - 24 q^{92} - 40 q^{94} - 4 q^{96} - 32 q^{97} + 88 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1320, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1320.2.w.a 1320.w 8.b $2$ $10.540$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}-iq^{3}+2iq^{4}-iq^{5}+\cdots\)
1320.2.w.b 1320.w 8.b $2$ $10.540$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}-iq^{3}+2iq^{4}-iq^{5}+\cdots\)
1320.2.w.c 1320.w 8.b $12$ $10.540$ \(\Q(\zeta_{28})\) None \(-2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{28}^{9}q^{2}-\zeta_{28}^{5}q^{3}-\zeta_{28}^{4}q^{4}+\cdots\)
1320.2.w.d 1320.w 8.b $18$ $10.540$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}-\beta _{11}q^{5}+\cdots\)
1320.2.w.e 1320.w 8.b $20$ $10.540$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{11}q^{5}+\cdots\)
1320.2.w.f 1320.w 8.b $26$ $10.540$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)