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Properties

Label 280.3.bb
Level $280$
Weight $3$
Character orbit 280.bb
Rep. character $\chi_{280}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
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.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
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 208 48 160
Cusp forms 176 48 128
Eisenstein series 32 0 32

Trace form

\( 48 q - 80 q^{9} + O(q^{10}) \) \( 48 q - 80 q^{9} + 4 q^{11} + 40 q^{15} + 36 q^{19} - 44 q^{21} + 28 q^{25} + 72 q^{29} - 120 q^{31} - 32 q^{35} - 32 q^{39} - 96 q^{45} + 168 q^{49} + 24 q^{51} + 240 q^{59} + 144 q^{61} + 32 q^{65} - 304 q^{71} + 288 q^{75} - 40 q^{79} - 540 q^{81} - 312 q^{85} - 108 q^{89} + 600 q^{91} - 352 q^{95} - 504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bb.a 280.bb 35.i $48$ $7.629$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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