Properties

Label 2240.2.l
Level $2240$
Weight $2$
Character orbit 2240.l
Rep. character $\chi_{2240}(1569,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $4$
Sturm bound $768$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(768\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2240, [\chi])\).

Total New Old
Modular forms 408 72 336
Cusp forms 360 72 288
Eisenstein series 48 0 48

Trace form

\( 72q + 72q^{9} + O(q^{10}) \) \( 72q + 72q^{9} - 24q^{25} + 48q^{41} - 72q^{49} + 48q^{65} + 72q^{81} + 48q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2240.2.l.a \(12\) \(17.886\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{9}q^{3}-\beta _{4}q^{5}+\beta _{3}q^{7}+(1+\beta _{4}+\cdots)q^{9}+\cdots\)
2240.2.l.b \(12\) \(17.886\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{9}q^{3}+\beta _{4}q^{5}-\beta _{3}q^{7}+(1+\beta _{4}+\cdots)q^{9}+\cdots\)
2240.2.l.c \(24\) \(17.886\) None \(0\) \(0\) \(-4\) \(0\)
2240.2.l.d \(24\) \(17.886\) None \(0\) \(0\) \(4\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)