Properties

Label 280.3.c
Level $280$
Weight $3$
Character orbit 280.c
Rep. character $\chi_{280}(69,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $7$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 280.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(17\), \(19\)

Dimensions

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

Total New Old
Modular forms 100 100 0
Cusp forms 92 92 0
Eisenstein series 8 8 0

Trace form

\( 92q - 4q^{4} - 260q^{9} + O(q^{10}) \) \( 92q - 4q^{4} - 260q^{9} - 20q^{14} + 32q^{15} + 20q^{16} - 4q^{25} - 84q^{30} - 132q^{36} + 64q^{39} - 40q^{44} - 224q^{46} - 4q^{49} + 156q^{50} + 92q^{56} - 292q^{60} + 140q^{64} + 96q^{65} + 72q^{70} + 248q^{71} + 144q^{74} - 8q^{79} + 572q^{81} + 408q^{84} + 96q^{86} + 280q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
280.3.c.a \(1\) \(7.629\) \(\Q\) \(\Q(\sqrt{-70}) \) \(-2\) \(0\) \(-5\) \(-7\) \(q-2q^{2}+4q^{4}-5q^{5}-7q^{7}-8q^{8}+\cdots\)
280.3.c.b \(1\) \(7.629\) \(\Q\) \(\Q(\sqrt{-70}) \) \(-2\) \(0\) \(5\) \(7\) \(q-2q^{2}+4q^{4}+5q^{5}+7q^{7}-8q^{8}+\cdots\)
280.3.c.c \(1\) \(7.629\) \(\Q\) \(\Q(\sqrt{-70}) \) \(2\) \(0\) \(-5\) \(7\) \(q+2q^{2}+4q^{4}-5q^{5}+7q^{7}+8q^{8}+\cdots\)
280.3.c.d \(1\) \(7.629\) \(\Q\) \(\Q(\sqrt{-70}) \) \(2\) \(0\) \(5\) \(-7\) \(q+2q^{2}+4q^{4}+5q^{5}-7q^{7}+8q^{8}+\cdots\)
280.3.c.e \(4\) \(7.629\) \(\Q(i, \sqrt{14})\) \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(-12\) \(0\) \(q+2\beta _{2}q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3})q^{3}-4q^{4}+\cdots\)
280.3.c.f \(4\) \(7.629\) \(\Q(i, \sqrt{14})\) \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(12\) \(0\) \(q-2\beta _{2}q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3})q^{3}-4q^{4}+\cdots\)
280.3.c.g \(80\) \(7.629\) None \(0\) \(0\) \(0\) \(0\)