↑

Properties

Label 490.2.l
Level $490$
Weight $2$
Character orbit 490.l
Rep. character $\chi_{490}(117,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $80$
Newform subspaces $4$
Sturm bound $168$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(168\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 400 80 320
Cusp forms 272 80 192
Eisenstein series 128 0 128

Trace form

\( 80 q + 12 q^{5} + O(q^{10}) \) \( 80 q + 12 q^{5} + 12 q^{10} + 20 q^{11} - 16 q^{15} + 40 q^{16} + 36 q^{17} + 16 q^{18} + 24 q^{22} + 4 q^{23} - 20 q^{25} - 12 q^{26} - 28 q^{30} - 24 q^{31} - 48 q^{33} - 104 q^{36} + 4 q^{37} - 24 q^{38} - 8 q^{43} + 12 q^{45} + 8 q^{46} - 12 q^{47} + 32 q^{50} + 16 q^{51} - 20 q^{53} - 8 q^{57} - 8 q^{58} - 16 q^{60} + 12 q^{61} + 16 q^{65} - 48 q^{67} + 36 q^{68} - 16 q^{71} + 16 q^{72} + 12 q^{73} + 48 q^{75} + 12 q^{80} + 64 q^{81} + 48 q^{82} - 8 q^{85} - 20 q^{86} + 24 q^{87} + 12 q^{88} - 8 q^{92} - 52 q^{93} - 12 q^{95} - 12 q^{96} + O(q^{100}) \)

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.l.a 490.l 35.k $16$ $3.913$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q-\zeta_{48}^{10}q^{2}+(-\zeta_{48}^{5}-\zeta_{48}^{7}+\zeta_{48}^{15})q^{3}+\cdots\)
490.2.l.b 490.l 35.k $16$ $3.913$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{48}^{14}q^{2}+(-\zeta_{48}-\zeta_{48}^{3}+\zeta_{48}^{7}+\cdots)q^{3}+\cdots\)
490.2.l.c 490.l 35.k $16$ $3.913$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{7}-\beta _{15})q^{2}+(\beta _{4}-\beta _{13})q^{3}+\cdots\)
490.2.l.d 490.l 35.k $32$ $3.913$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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