Properties

Label 490.2.g
Level $490$
Weight $2$
Character orbit 490.g
Rep. character $\chi_{490}(97,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $3$
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.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
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 200 40 160
Cusp forms 136 40 96
Eisenstein series 64 0 64

Trace form

\( 40 q + O(q^{10}) \) \( 40 q - 8 q^{11} + 16 q^{15} - 40 q^{16} - 16 q^{18} + 24 q^{22} + 8 q^{23} + 8 q^{25} - 8 q^{30} - 64 q^{36} - 40 q^{37} - 40 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 80 q^{53} + 8 q^{57} + 56 q^{58} + 16 q^{60} - 16 q^{65} + 16 q^{71} - 16 q^{72} + 48 q^{78} - 88 q^{81} + 56 q^{85} + 8 q^{86} - 24 q^{88} + 8 q^{92} + 40 q^{93} - 72 q^{95} + O(q^{100}) \)

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.g.a \(8\) \(3.913\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{2}+(-\zeta_{16}-\zeta_{16}^{3}-\zeta_{16}^{5}+\cdots)q^{3}+\cdots\)
490.2.g.b \(16\) \(3.913\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}+(-\beta _{11}-\beta _{12}+\beta _{13})q^{3}+\cdots\)
490.2.g.c \(16\) \(3.913\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(-\beta _{8}+\beta _{14})q^{3}-\beta _{9}q^{4}+\cdots\)

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

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