Properties

Label 280.3.f
Level $280$
Weight $3$
Character orbit 280.f
Rep. character $\chi_{280}(41,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 280.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(280, [\chi])\).

Total New Old
Modular forms 104 16 88
Cusp forms 88 16 72
Eisenstein series 16 0 16

Trace form

\( 16 q - 16 q^{7} - 64 q^{9} + O(q^{10}) \) \( 16 q - 16 q^{7} - 64 q^{9} - 8 q^{11} + 60 q^{21} - 80 q^{25} - 136 q^{29} - 20 q^{35} - 144 q^{37} - 192 q^{39} + 272 q^{43} + 68 q^{49} - 144 q^{51} + 240 q^{53} - 48 q^{57} + 104 q^{63} - 120 q^{65} + 48 q^{67} + 344 q^{71} + 360 q^{77} + 8 q^{79} + 120 q^{81} - 280 q^{91} - 208 q^{93} - 40 q^{95} + 568 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
280.3.f.a 280.f 7.b $16$ $7.629$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{10}q^{5}+(-1-\beta _{8})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)