Properties

Label 2240.2.k
Level $2240$
Weight $2$
Character orbit 2240.k
Rep. character $\chi_{2240}(1791,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $7$
Sturm bound $768$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(768\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(19\)

Dimensions

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

Total New Old
Modular forms 408 64 344
Cusp forms 360 64 296
Eisenstein series 48 0 48

Trace form

\( 64q + 64q^{9} + O(q^{10}) \) \( 64q + 64q^{9} - 16q^{21} - 64q^{25} + 16q^{29} - 16q^{37} - 16q^{53} + 96q^{81} + 32q^{93} + O(q^{100}) \)

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.k.a \(4\) \(17.886\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}+(2\zeta_{12}+\zeta_{12}^{3})q^{7}+\cdots\)
2240.2.k.b \(4\) \(17.886\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}+(-2\zeta_{12}+\zeta_{12}^{3})q^{7}+\cdots\)
2240.2.k.c \(8\) \(17.886\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)
2240.2.k.d \(8\) \(17.886\) 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{3}-\beta _{3}q^{5}+(-\beta _{4}+\beta _{6})q^{7}+\cdots\)
2240.2.k.e \(8\) \(17.886\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{5})q^{3}+\beta _{1}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
2240.2.k.f \(16\) \(17.886\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{9}q^{3}+\beta _{4}q^{5}-\beta _{11}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.2.k.g \(16\) \(17.886\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{9}q^{3}+\beta _{4}q^{5}+\beta _{11}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)