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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
490.2.e.a 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.b 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.c 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+q^{8}+\cdots\)
490.2.e.d 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+q^{8}+\cdots\)
490.2.e.e 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.f 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.g 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.h 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.i 490.e 7.c $4$ $3.913$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3})q^{3}+\cdots\)
490.2.e.j 490.e 7.c $4$ $3.913$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(2+\beta _{1}+2\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)

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

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