Properties

Label 280.2.bv
Level $280$
Weight $2$
Character orbit 280.bv
Rep. character $\chi_{280}(117,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $176$
Newform subspaces $5$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

Trace form

\( 176q - 2q^{2} - 8q^{7} + 4q^{8} + O(q^{10}) \) \( 176q - 2q^{2} - 8q^{7} + 4q^{8} - 6q^{10} - 6q^{12} - 16q^{15} - 12q^{16} - 12q^{17} - 16q^{18} - 16q^{22} - 4q^{23} - 4q^{25} - 12q^{26} - 50q^{28} + 8q^{30} - 24q^{31} + 18q^{32} - 12q^{33} - 48q^{36} - 24q^{38} + 54q^{40} - 10q^{42} - 28q^{46} - 84q^{47} - 12q^{50} + 72q^{52} - 20q^{56} - 40q^{57} + 2q^{58} + 46q^{60} - 24q^{63} - 4q^{65} - 156q^{66} + 60q^{68} - 112q^{70} + 32q^{71} + 52q^{72} - 12q^{73} - 24q^{78} + 48q^{80} - 54q^{82} - 72q^{86} - 48q^{87} + 60q^{88} + 12q^{92} - 20q^{95} - 96q^{96} - 130q^{98} + O(q^{100}) \)

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.bv.a \(4\) \(2.236\) \(\Q(\zeta_{12})\) None \(-4\) \(-2\) \(-4\) \(-10\) \(q+(-1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
280.2.bv.b \(4\) \(2.236\) \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(4\) \(-10\) \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
280.2.bv.c \(4\) \(2.236\) \(\Q(\zeta_{12})\) None \(2\) \(-4\) \(4\) \(0\) \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\)
280.2.bv.d \(4\) \(2.236\) \(\Q(\zeta_{12})\) None \(4\) \(4\) \(-4\) \(0\) \(q+(1-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
280.2.bv.e \(160\) \(2.236\) None \(-2\) \(0\) \(0\) \(12\)