Properties

Label 240.2.v
Level $240$
Weight $2$
Character orbit 240.v
Rep. character $\chi_{240}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $5$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).

Total New Old
Modular forms 120 28 92
Cusp forms 72 20 52
Eisenstein series 48 8 40

Trace form

\( 20 q + 2 q^{3} + 4 q^{7} + O(q^{10}) \) \( 20 q + 2 q^{3} + 4 q^{7} - 4 q^{13} + 14 q^{15} - 12 q^{21} - 4 q^{25} + 14 q^{27} + 4 q^{33} - 20 q^{37} - 12 q^{43} - 12 q^{45} - 20 q^{51} - 40 q^{55} + 20 q^{57} - 24 q^{61} - 48 q^{63} - 20 q^{67} + 4 q^{73} - 38 q^{75} + 4 q^{81} - 20 q^{85} - 20 q^{87} + 56 q^{91} - 8 q^{93} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.2.v.a 240.v 15.e $4$ $1.916$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\zeta_{8}^{2})q^{3}+(1+2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots\)
240.2.v.b 240.v 15.e $4$ $1.916$ \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{3})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
240.2.v.c 240.v 15.e $4$ $1.916$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1-2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots\)
240.2.v.d 240.v 15.e $4$ $1.916$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
240.2.v.e 240.v 15.e $4$ $1.916$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)