Properties

Label 2240.2.h
Level $2240$
Weight $2$
Character orbit 2240.h
Rep. character $\chi_{2240}(671,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $6$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(768\)
Trace bound: \(9\)
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 64 344
Cusp forms 360 64 296
Eisenstein series 48 0 48

Trace form

\( 64q - 64q^{9} + O(q^{10}) \) \( 64q - 64q^{9} + 64q^{25} + 32q^{49} + 64q^{57} - 32q^{81} + O(q^{100}) \)

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.h.a \(4\) \(17.886\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}-q^{5}+(\beta _{1}+\beta _{2})q^{7}-q^{9}+\cdots\)
2240.2.h.b \(4\) \(17.886\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{12}q^{3}-q^{5}+(2\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
2240.2.h.c \(4\) \(17.886\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{1}q^{3}+q^{5}+(\beta _{1}+\beta _{2})q^{7}-q^{9}+\cdots\)
2240.2.h.d \(4\) \(17.886\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{12}q^{3}+q^{5}+(-2\zeta_{12}+\zeta_{12}^{3})q^{7}+\cdots\)
2240.2.h.e \(24\) \(17.886\) None \(0\) \(0\) \(-24\) \(0\)
2240.2.h.f \(24\) \(17.886\) None \(0\) \(0\) \(24\) \(0\)

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)