Properties

Label 980.2.q
Level $980$
Weight $2$
Character orbit 980.q
Rep. character $\chi_{980}(569,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $9$
Sturm bound $336$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(980, [\chi])\).

Total New Old
Modular forms 384 40 344
Cusp forms 288 40 248
Eisenstein series 96 0 96

Trace form

\( 40 q + q^{5} + 26 q^{9} + O(q^{10}) \) \( 40 q + q^{5} + 26 q^{9} - 8 q^{11} + 14 q^{15} + 2 q^{19} + 15 q^{25} + 8 q^{29} - 2 q^{31} + 18 q^{39} + 60 q^{41} + 20 q^{51} - 54 q^{55} - 2 q^{59} - 24 q^{61} + 6 q^{65} - 48 q^{69} - 56 q^{71} + 27 q^{75} - 16 q^{79} - 76 q^{81} - 22 q^{85} + 28 q^{89} + 35 q^{95} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.2.q.a 980.q 35.j $4$ $7.825$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2-\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
980.2.q.b 980.q 35.j $4$ $7.825$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(-6\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
980.2.q.c 980.q 35.j $4$ $7.825$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+3\zeta_{12}q^{3}+(-\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
980.2.q.d 980.q 35.j $4$ $7.825$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}-3\zeta_{12}^{2}q^{9}+\cdots\)
980.2.q.e 980.q 35.j $4$ $7.825$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}-3\zeta_{12}^{2}q^{9}+\cdots\)
980.2.q.f 980.q 35.j $4$ $7.825$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+3\zeta_{12}q^{3}+(-\zeta_{12}+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
980.2.q.g 980.q 35.j $4$ $7.825$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(6\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\beta _{2})q^{3}+\beta _{3}q^{5}+(1-2\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
980.2.q.h 980.q 35.j $4$ $7.825$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(6\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2})q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
980.2.q.i 980.q 35.j $8$ $7.825$ 8.0.\(\cdots\).2 \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(\beta _{2}-\beta _{7})q^{3}+(-\beta _{3}-\beta _{7})q^{5}+(4+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)