Properties

Label 240.2.w
Level $240$
Weight $2$
Character orbit 240.w
Rep. character $\chi_{240}(127,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 120 12 108
Cusp forms 72 12 60
Eisenstein series 48 0 48

Trace form

\( 12q + O(q^{10}) \) \( 12q + 12q^{13} + 12q^{17} + 12q^{25} - 24q^{33} - 12q^{37} - 48q^{41} - 12q^{45} - 12q^{53} - 12q^{65} + 12q^{73} - 48q^{77} - 12q^{81} - 36q^{85} + 48q^{93} + 12q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
240.2.w.a \(4\) \(1.916\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q+\zeta_{8}q^{3}+(-2+\zeta_{8}^{2})q^{5}+4\zeta_{8}^{3}q^{7}+\cdots\)
240.2.w.b \(8\) \(1.916\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(8\) \(0\) \(q+\zeta_{24}^{5}q^{3}+(1+\zeta_{24}^{2}-\zeta_{24}^{3})q^{5}+\cdots\)

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

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