Properties

Label 490.4.c
Level $490$
Weight $4$
Character orbit 490.c
Rep. character $\chi_{490}(99,\cdot)$
Character field $\Q$
Dimension $62$
Newform subspaces $7$
Sturm bound $336$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 490.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(490, [\chi])\).

Total New Old
Modular forms 268 62 206
Cusp forms 236 62 174
Eisenstein series 32 0 32

Trace form

\( 62 q - 248 q^{4} + 6 q^{5} - 8 q^{6} - 530 q^{9} + O(q^{10}) \) \( 62 q - 248 q^{4} + 6 q^{5} - 8 q^{6} - 530 q^{9} + 16 q^{10} + 100 q^{11} - 44 q^{15} + 992 q^{16} - 24 q^{19} - 24 q^{20} + 32 q^{24} - 514 q^{25} - 416 q^{26} + 104 q^{29} + 352 q^{30} + 184 q^{31} + 528 q^{34} + 2120 q^{36} + 680 q^{39} - 64 q^{40} - 884 q^{41} - 400 q^{44} - 1318 q^{45} + 744 q^{46} + 1240 q^{50} + 544 q^{51} + 1616 q^{54} - 1176 q^{55} + 1136 q^{59} + 176 q^{60} + 92 q^{61} - 3968 q^{64} + 208 q^{65} - 192 q^{66} + 5248 q^{69} - 864 q^{71} - 56 q^{74} + 2960 q^{75} + 96 q^{76} - 4120 q^{79} + 96 q^{80} + 2038 q^{81} - 384 q^{85} + 1008 q^{86} - 3516 q^{89} - 3968 q^{90} + 72 q^{94} - 1236 q^{95} - 128 q^{96} - 3068 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(490, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
490.4.c.a 490.c 5.b $2$ $28.911$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2iq^{2}+7iq^{3}-4q^{4}+(-10+5i)q^{5}+\cdots\)
490.4.c.b 490.c 5.b $2$ $28.911$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-4q^{4}+(5+5i)q^{5}+\cdots\)
490.4.c.c 490.c 5.b $6$ $28.911$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{3}q^{2}+(2\beta _{3}-\beta _{5})q^{3}-4q^{4}+(3+\cdots)q^{5}+\cdots\)
490.4.c.d 490.c 5.b $8$ $28.911$ 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}-4q^{4}+(-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
490.4.c.e 490.c 5.b $12$ $28.911$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}+(\beta _{4}+\beta _{7})q^{3}-4q^{4}+(-1+\cdots)q^{5}+\cdots\)
490.4.c.f 490.c 5.b $12$ $28.911$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+(\beta _{4}+\beta _{7})q^{3}-4q^{4}+(1-\beta _{5}+\cdots)q^{5}+\cdots\)
490.4.c.g 490.c 5.b $20$ $28.911$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+\beta _{5}q^{3}-4q^{4}+\beta _{8}q^{5}-\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(490, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)