Properties

Label 2240.2.b
Level $2240$
Weight $2$
Character orbit 2240.b
Rep. character $\chi_{2240}(1121,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $8$
Sturm bound $768$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(768\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(23\), \(31\)

Dimensions

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

Total New Old
Modular forms 408 48 360
Cusp forms 360 48 312
Eisenstein series 48 0 48

Trace form

\( 48q - 48q^{9} + O(q^{10}) \) \( 48q - 48q^{9} - 48q^{25} + 96q^{33} - 96q^{41} + 48q^{49} - 96q^{57} + 144q^{81} + O(q^{100}) \)

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.b.a \(2\) \(17.886\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{5}-q^{7}+3q^{9}-2iq^{11}-2iq^{13}+\cdots\)
2240.2.b.b \(2\) \(17.886\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{5}+q^{7}+3q^{9}+2iq^{11}-2iq^{13}+\cdots\)
2240.2.b.c \(4\) \(17.886\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-q^{7}-\zeta_{12}q^{11}+\cdots\)
2240.2.b.d \(4\) \(17.886\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+q^{7}+\zeta_{12}q^{11}+\cdots\)
2240.2.b.e \(6\) \(17.886\) 6.0.3534400.1 None \(0\) \(0\) \(0\) \(-6\) \(q-\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.2.b.f \(6\) \(17.886\) 6.0.3534400.1 None \(0\) \(0\) \(0\) \(6\) \(q-\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.2.b.g \(12\) \(17.886\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-12\) \(q-\beta _{11}q^{3}+\beta _{9}q^{5}-q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
2240.2.b.h \(12\) \(17.886\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(12\) \(q-\beta _{11}q^{3}-\beta _{9}q^{5}+q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)