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Properties

Label 490.2.i
Level $490$
Weight $2$
Character orbit 490.i
Rep. character $\chi_{490}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $6$
Sturm bound $168$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(168\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(11\), \(19\)

Dimensions

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

Total New Old
Modular forms 200 40 160
Cusp forms 136 40 96
Eisenstein series 64 0 64

Trace form

\( 40 q + 20 q^{4} - 2 q^{5} + 12 q^{6} + 14 q^{9} + O(q^{10}) \) \( 40 q + 20 q^{4} - 2 q^{5} + 12 q^{6} + 14 q^{9} - 2 q^{10} + 10 q^{11} + 32 q^{15} - 20 q^{16} + 14 q^{19} - 4 q^{20} + 6 q^{24} - 14 q^{26} - 28 q^{29} - 6 q^{30} + 16 q^{31} - 16 q^{34} + 28 q^{36} - 12 q^{39} + 2 q^{40} - 10 q^{44} - 24 q^{45} - 24 q^{46} + 20 q^{51} + 18 q^{54} + 24 q^{55} + 4 q^{59} + 16 q^{60} - 6 q^{61} - 40 q^{64} + 30 q^{65} + 12 q^{69} + 16 q^{71} - 30 q^{74} - 24 q^{75} + 28 q^{76} - 16 q^{79} - 2 q^{80} + 20 q^{81} - 64 q^{85} + 18 q^{86} + 10 q^{89} - 60 q^{90} - 2 q^{94} - 28 q^{95} - 6 q^{96} - 60 q^{99} + O(q^{100}) \)

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.i.a 490.i 35.j $4$ $3.913$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}+\cdots)q^{5}+\cdots\)
490.2.i.b 490.i 35.j $4$ $3.913$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
490.2.i.c 490.i 35.j $8$ $3.913$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{4})q^{2}+(-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
490.2.i.d 490.i 35.j $8$ $3.913$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
490.2.i.e 490.i 35.j $8$ $3.913$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{2}q^{2}+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
490.2.i.f 490.i 35.j $8$ $3.913$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{4})q^{2}+(-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)

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

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