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Properties

Label 240.4.v
Level $240$
Weight $4$
Character orbit 240.v
Rep. character $\chi_{240}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $5$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(240, [\chi])\).

Total New Old
Modular forms 312 76 236
Cusp forms 264 68 196
Eisenstein series 48 8 40

Trace form

\( 68 q + 2 q^{3} + 4 q^{7} + O(q^{10}) \) \( 68 q + 2 q^{3} + 4 q^{7} - 4 q^{13} + 14 q^{15} + 132 q^{21} - 4 q^{25} + 446 q^{27} - 256 q^{31} + 52 q^{33} + 524 q^{37} + 436 q^{43} - 252 q^{45} - 308 q^{51} + 440 q^{55} - 796 q^{57} + 904 q^{61} + 1008 q^{63} + 76 q^{67} + 980 q^{73} - 518 q^{75} - 620 q^{81} - 1780 q^{85} + 700 q^{87} - 1288 q^{91} - 56 q^{93} - 748 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.4.v.a 240.v 15.e $4$ $14.160$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(-92\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
240.4.v.b 240.v 15.e $8$ $14.160$ 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(80\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}+(\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
240.4.v.c 240.v 15.e $8$ $14.160$ 8.0.\(\cdots\).8 None \(0\) \(6\) \(0\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
240.4.v.d 240.v 15.e $12$ $14.160$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-8\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{3}+\beta _{9})q^{3}+(1+\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
240.4.v.e 240.v 15.e $36$ $14.160$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)