Properties

Label 240.4.w
Level $240$
Weight $4$
Character orbit 240.w
Rep. character $\chi_{240}(127,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $36$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 240.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)
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 36 276
Cusp forms 264 36 228
Eisenstein series 48 0 48

Trace form

\( 36 q + O(q^{10}) \) \( 36 q + 276 q^{13} - 156 q^{17} + 132 q^{25} - 72 q^{33} + 396 q^{37} + 1776 q^{41} + 108 q^{45} - 1716 q^{53} - 1572 q^{65} + 3396 q^{73} + 3504 q^{77} - 2916 q^{81} + 3684 q^{85} - 2736 q^{93} - 4956 q^{97} + O(q^{100}) \)

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.w.a 240.w 20.e $12$ $14.160$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(32\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(3+\beta _{8})q^{5}+(2\beta _{3}-\beta _{4}+\beta _{10}+\cdots)q^{7}+\cdots\)
240.4.w.b 240.w 20.e $24$ $14.160$ None \(0\) \(0\) \(-32\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{4}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)