Space of modular forms of level 980, weight 2, and Character 980.q

• 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: $5$

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 - 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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
980.2.q.a	$980$	$2$	980.q	35.j	$6$	$4$	$2$	$7.825$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			980.2.e.e	$4$	$0$	\(0\)	\(-6\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2-\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
980.2.q.b	$980$	$2$	980.q	35.j	$6$	$4$	$2$	$7.825$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					140.2.q.a	$2$	$0$	\(0\)	\(-6\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
980.2.q.c	$980$	$2$	980.q	35.j	$6$	$4$	$2$	$7.825$	\(\Q(\zeta_{12})\)	None					140.2.e.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{12}q^{3}+(-\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
980.2.q.d	$980$	$2$	980.q	35.j	$6$	$4$	$2$	$7.825$	\(\Q(\zeta_{12})\)	None					140.2.e.b	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta_{3}-\beta_{2}+\beta_1)q^{5}-3\beta_{2} q^{9}+\cdots\)
980.2.q.e	$980$	$2$	980.q	35.j	$6$	$4$	$2$	$7.825$	\(\Q(\zeta_{12})\)	None					140.2.e.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{3}+\beta_{2}-\beta_1)q^{5}-3\beta_{2} q^{9}+\cdots\)
980.2.q.f	$980$	$2$	980.q	35.j	$6$	$4$	$2$	$7.825$	\(\Q(\zeta_{12})\)	None					140.2.e.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{12}q^{3}+(-\zeta_{12}+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
980.2.q.g	$980$	$2$	980.q	35.j	$6$	$4$	$2$	$7.825$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					140.2.q.a	$2$	$0$	\(0\)	\(6\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\beta _{2})q^{3}+\beta _{3}q^{5}+(1-2\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
980.2.q.h	$980$	$2$	980.q	35.j	$6$	$4$	$2$	$7.825$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			980.2.e.e	$4$	$0$	\(0\)	\(6\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2})q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
980.2.q.i	$980$	$2$	980.q	35.j	$6$	$8$	$4$	$7.825$	8.0.\(\cdots\).2	\(\Q(\sqrt{-35}) \)		✓	✓		980.2.e.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+(\beta _{2}-\beta _{7})q^{3}+(-\beta _{3}-\beta _{7})q^{5}+(4+\cdots)q^{9}+\cdots\)

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

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