Properties

Label 2240.1.p
Level $2240$
Weight $1$
Character orbit 2240.p
Rep. character $\chi_{2240}(769,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $5$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2240.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(384\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2240, [\chi])\).

Total New Old
Modular forms 56 12 44
Cusp forms 32 8 24
Eisenstein series 24 4 20

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2240.1.p.a \(1\) \(1.118\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q-q^{3}-q^{5}-q^{7}-q^{11}+q^{13}+q^{15}+\cdots\)
2240.1.p.b \(1\) \(1.118\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(1\) \(-1\) \(q-q^{3}+q^{5}-q^{7}+q^{11}-q^{13}-q^{15}+\cdots\)
2240.1.p.c \(1\) \(1.118\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(-1\) \(1\) \(q+q^{3}-q^{5}+q^{7}+q^{11}+q^{13}-q^{15}+\cdots\)
2240.1.p.d \(1\) \(1.118\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(1\) \(1\) \(q+q^{3}+q^{5}+q^{7}-q^{11}-q^{13}+q^{15}+\cdots\)
2240.1.p.e \(4\) \(1.118\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)