Properties

Label 2240.2.n
Level $2240$
Weight $2$
Character orbit 2240.n
Rep. character $\chi_{2240}(1119,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $10$
Sturm bound $768$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(768\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(11\), \(17\), \(23\)

Dimensions

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

Total New Old
Modular forms 408 96 312
Cusp forms 360 96 264
Eisenstein series 48 0 48

Trace form

\( 96q + 96q^{9} + O(q^{10}) \) \( 96q + 96q^{9} + 192q^{81} + O(q^{100}) \)

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.n.a \(8\) \(17.886\) 8.0.1731891456.1 None \(0\) \(-4\) \(-16\) \(16\) \(q+(-1+\beta _{1})q^{3}+(-2-\beta _{5})q^{5}+(2+\cdots)q^{7}+\cdots\)
2240.2.n.b \(8\) \(17.886\) 8.0.1731891456.1 None \(0\) \(-4\) \(16\) \(-16\) \(q+(-1+\beta _{1})q^{3}+(2+\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots\)
2240.2.n.c \(8\) \(17.886\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{5}-\zeta_{24}^{4}q^{7}-3q^{9}+2\zeta_{24}q^{11}+\cdots\)
2240.2.n.d \(8\) \(17.886\) 8.0.384160000.1 \(\Q(\sqrt{-70}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}-\beta _{3}q^{7}-3q^{9}-\beta _{2}q^{17}+\cdots\)
2240.2.n.e \(8\) \(17.886\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{5}+(-\zeta_{24}^{2}-\zeta_{24}^{4})q^{7}+\cdots\)
2240.2.n.f \(8\) \(17.886\) 8.0.384160000.1 \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{3}q^{7}+2q^{9}-\beta _{5}q^{11}+\cdots\)
2240.2.n.g \(8\) \(17.886\) 8.0.1731891456.1 None \(0\) \(4\) \(-16\) \(-16\) \(q+\beta _{1}q^{3}+(-2+\beta _{5})q^{5}+(-2-\beta _{2}+\cdots)q^{7}+\cdots\)
2240.2.n.h \(8\) \(17.886\) 8.0.1731891456.1 None \(0\) \(4\) \(16\) \(16\) \(q+\beta _{1}q^{3}+(2+\beta _{5})q^{5}+(2+\beta _{2})q^{7}+\cdots\)
2240.2.n.i \(16\) \(17.886\) 16.0.\(\cdots\).7 \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{6}-\beta _{7})q^{3}-\beta _{11}q^{5}-\beta _{3}q^{7}+(3+\cdots)q^{9}+\cdots\)
2240.2.n.j \(16\) \(17.886\) 16.0.\(\cdots\).1 \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{7}q^{5}+(\beta _{2}-\beta _{9})q^{7}+(3+\cdots)q^{9}+\cdots\)

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

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