Properties

Label 280.2.g
Level $280$
Weight $2$
Character orbit 280.g
Rep. character $\chi_{280}(169,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 56 8 48
Cusp forms 40 8 32
Eisenstein series 16 0 16

Trace form

\( 8q + 4q^{5} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{5} - 4q^{9} + 12q^{11} - 16q^{15} - 4q^{21} - 4q^{25} - 4q^{29} + 8q^{31} + 12q^{39} + 16q^{41} - 20q^{45} - 8q^{49} + 36q^{51} - 16q^{55} - 24q^{59} + 40q^{61} - 24q^{65} - 40q^{69} - 24q^{71} - 32q^{75} - 12q^{79} + 32q^{81} + 20q^{85} - 24q^{89} + 12q^{91} + 12q^{95} - 8q^{99} + O(q^{100}) \)

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.g.a \(2\) \(2.236\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+(2-i)q^{5}+iq^{7}+2q^{9}-q^{11}+\cdots\)
280.2.g.b \(6\) \(2.236\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(\beta _{1}-\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)