Properties

Label 490.2.e
Level $490$
Weight $2$
Character orbit 490.e
Rep. character $\chi_{490}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $10$
Sturm bound $168$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(168\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(490, [\chi])\).

Total New Old
Modular forms 200 24 176
Cusp forms 136 24 112
Eisenstein series 64 0 64

Trace form

\( 24q - 12q^{4} - 2q^{5} - 4q^{6} - 14q^{9} + O(q^{10}) \) \( 24q - 12q^{4} - 2q^{5} - 4q^{6} - 14q^{9} - 2q^{10} - 6q^{11} + 16q^{15} - 12q^{16} - 4q^{17} + 8q^{18} - 6q^{19} + 4q^{20} - 8q^{22} + 12q^{23} + 2q^{24} - 12q^{25} + 10q^{26} - 24q^{27} - 4q^{29} + 2q^{30} + 8q^{31} - 24q^{33} - 16q^{34} + 28q^{36} + 52q^{37} - 8q^{38} + 36q^{39} - 2q^{40} - 16q^{41} - 56q^{43} - 6q^{44} - 4q^{45} - 8q^{46} + 20q^{47} - 44q^{51} - 12q^{53} + 14q^{54} - 16q^{55} - 56q^{57} - 8q^{58} + 4q^{59} - 8q^{60} + 10q^{61} + 48q^{62} + 24q^{64} - 6q^{65} + 48q^{67} - 4q^{68} + 36q^{69} + 32q^{71} + 8q^{72} - 28q^{73} + 14q^{74} + 12q^{76} + 64q^{78} + 32q^{79} - 2q^{80} - 76q^{81} - 16q^{82} + 32q^{83} + 40q^{85} - 30q^{86} + 24q^{87} + 4q^{88} - 2q^{89} + 20q^{90} - 24q^{92} + 12q^{93} + 2q^{94} + 2q^{96} - 64q^{97} - 132q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(490, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
490.2.e.a \(2\) \(3.913\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.b \(2\) \(3.913\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.c \(2\) \(3.913\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+q^{8}+\cdots\)
490.2.e.d \(2\) \(3.913\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+q^{8}+\cdots\)
490.2.e.e \(2\) \(3.913\) \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.f \(2\) \(3.913\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.g \(2\) \(3.913\) \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(1\) \(0\) \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.h \(2\) \(3.913\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.i \(4\) \(3.913\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-4\) \(-2\) \(0\) \(q+(1+\beta _{2})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3})q^{3}+\cdots\)
490.2.e.j \(4\) \(3.913\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(4\) \(2\) \(0\) \(q-\beta _{2}q^{2}+(2+\beta _{1}+2\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(490, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)