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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
280.2.g.a 280.g 5.b $2$ $2.236$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(2-i)q^{5}+iq^{7}+2q^{9}-q^{11}+\cdots\)
280.2.g.b 280.g 5.b $6$ $2.236$ 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(\beta _{1}-\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)

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

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