Properties

Label 2240.2.e
Level $2240$
Weight $2$
Character orbit 2240.e
Rep. character $\chi_{2240}(2239,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $7$
Sturm bound $768$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(768\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

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

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92q - 92q^{9} + O(q^{10}) \) \( 92q - 92q^{9} - 8q^{21} - 4q^{25} + 8q^{29} - 4q^{49} - 24q^{65} + 44q^{81} - 24q^{85} + O(q^{100}) \)

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.e.a \(4\) \(17.886\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}+\beta _{2})q^{3}-\beta _{3}q^{5}+(\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
2240.2.e.b \(4\) \(17.886\) \(\Q(\sqrt{5}, \sqrt{-7})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}-4q^{9}+\beta _{3}q^{11}+\cdots\)
2240.2.e.c \(4\) \(17.886\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2240.2.e.d \(8\) \(17.886\) 8.0.121550625.1 \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(-3+\cdots)q^{9}+\cdots\)
2240.2.e.e \(8\) \(17.886\) 8.0.\(\cdots\).5 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+\beta _{4}q^{5}-\beta _{1}q^{7}+q^{9}+2\beta _{3}q^{11}+\cdots\)
2240.2.e.f \(16\) \(17.886\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{3}-\beta _{10}q^{5}+(-\beta _{6}+\beta _{8})q^{7}+\cdots\)
2240.2.e.g \(48\) \(17.886\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)