Properties

Label 280.2.b
Level $280$
Weight $2$
Character orbit 280.b
Rep. character $\chi_{280}(141,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $4$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(280, [\chi])\).

Total New Old
Modular forms 52 24 28
Cusp forms 44 24 20
Eisenstein series 8 0 8

Trace form

\( 24q + 2q^{2} + 2q^{4} - 8q^{6} + 4q^{7} + 14q^{8} - 24q^{9} + O(q^{10}) \) \( 24q + 2q^{2} + 2q^{4} - 8q^{6} + 4q^{7} + 14q^{8} - 24q^{9} - 4q^{10} - 12q^{12} - 2q^{14} - 8q^{15} - 14q^{16} + 2q^{18} + 8q^{22} + 16q^{23} - 20q^{24} - 24q^{25} - 4q^{26} + 10q^{28} + 16q^{30} + 16q^{31} - 18q^{32} - 16q^{33} - 8q^{34} - 2q^{36} + 20q^{38} - 48q^{39} + 16q^{40} + 16q^{41} + 36q^{44} - 32q^{46} + 44q^{48} + 24q^{49} - 2q^{50} + 24q^{52} + 36q^{54} - 2q^{56} + 16q^{57} - 12q^{58} + 4q^{60} - 16q^{62} - 20q^{63} + 2q^{64} + 68q^{66} - 76q^{68} + 8q^{71} - 22q^{72} - 8q^{74} - 20q^{76} + 4q^{78} + 24q^{79} + 8q^{81} - 52q^{82} + 28q^{84} - 68q^{86} + 48q^{87} - 36q^{88} + 16q^{90} + 20q^{94} - 32q^{95} + 12q^{96} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
280.2.b.a \(2\) \(2.236\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+(1+i)q^{2}+2iq^{3}+2iq^{4}-iq^{5}+\cdots\)
280.2.b.b \(2\) \(2.236\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(2\) \(q+(1+i)q^{2}+2iq^{3}+2iq^{4}+iq^{5}+\cdots\)
280.2.b.c \(8\) \(2.236\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{6}q^{2}+(-\beta _{5}+\beta _{7})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
280.2.b.d \(12\) \(2.236\) 12.0.\(\cdots\).1 None \(-2\) \(0\) \(0\) \(12\) \(q+\beta _{6}q^{2}+(\beta _{1}-\beta _{3}+\beta _{7})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)