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

• Label: 980.2.x
• Level: $980$
• Weight: $2$
• Character orbit: 980.x
• Rep. character: $\chi_{980}(67,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $448$
• Newform subspaces: $14$
• Sturm bound: $336$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(336\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	736	512	224
Cusp forms	608	448	160
Eisenstein series	128	64	64

Trace form

448 * q + 2 * q^2 + 4 * q^5 + 16 * q^6 - 4 * q^8 + 2 * q^10 - 10 * q^12 + 16 * q^13 + 12 * q^16 + 4 * q^17 - 20 * q^18 + 24 * q^20 - 8 * q^22 + 4 * q^25 - 12 * q^26 + 52 * q^30 + 42 * q^32 + 36 * q^33 + 4 * q^37 - 12 * q^38 + 22 * q^40 + 16 * q^41 + 44 * q^45 + 52 * q^46 - 12 * q^48 + 100 * q^50 - 64 * q^52 + 4 * q^53 - 120 * q^57 - 66 * q^58 + 30 * q^60 + 8 * q^61 - 56 * q^62 + 36 * q^65 - 100 * q^66 - 4 * q^68 - 60 * q^72 + 20 * q^73 - 112 * q^76 - 280 * q^78 - 36 * q^80 + 144 * q^81 + 46 * q^82 - 80 * q^85 - 88 * q^86 - 40 * q^88 - 64 * q^90 - 68 * q^92 - 12 * q^93 + 48 * q^96 + 96 * q^97

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.x.a	$980$	$2$	980.x	140.w	$12$	$4$	$1$	$7.825$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			980.2.k.b	$8$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
980.2.x.b	$980$	$2$	980.x	140.w	$12$	$4$	$1$	$7.825$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			980.2.k.b	$8$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
980.2.x.c	$980$	$2$	980.x	140.w	$12$	$4$	$1$	$7.825$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)					20.2.e.a	$8$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
980.2.x.d	$980$	$2$	980.x	140.w	$12$	$4$	$1$	$7.825$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)					20.2.e.a	$8$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
980.2.x.e	$980$	$2$	980.x	140.w	$12$	$8$	$2$	$7.825$	\(\Q(\zeta_{24})\)	None		✓			980.2.k.h	$8$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\zeta_{24}^{6})q^{2}+(2\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
980.2.x.f	$980$	$2$	980.x	140.w	$12$	$8$	$2$	$7.825$	\(\Q(i, \sqrt{3}, \sqrt{14})\)	None					140.2.w.a	$8$	$0$	\(-4\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{2}-\beta _{4}+\beta _{6})q^{2}+\beta _{5}q^{3}+2\beta _{2}q^{4}+\cdots\)
980.2.x.g	$980$	$2$	980.x	140.w	$12$	$8$	$2$	$7.825$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-1}) \)		✓			980.2.k.f	$16$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-1-\zeta_{24}^{2}+\zeta_{24}^{4})q^{2}+(2\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
980.2.x.h	$980$	$2$	980.x	140.w	$12$	$8$	$2$	$7.825$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-1}) \)		✓			980.2.k.d	$16$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(1-\zeta_{24}^{2}-\zeta_{24}^{4})q^{2}+(-2\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
980.2.x.i	$980$	$2$	980.x	140.w	$12$	$8$	$2$	$7.825$	\(\Q(\zeta_{24})\)	None		✓			980.2.k.h	$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{24}^{2}-\zeta_{24}^{4})q^{2}+(2\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
980.2.x.j	$980$	$2$	980.x	140.w	$12$	$64$	$16$	$7.825$		None		✓			980.2.k.i	$16$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
980.2.x.k	$980$	$2$	980.x	140.w	$12$	$72$	$18$	$7.825$		None					140.2.k.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
980.2.x.l	$980$	$2$	980.x	140.w	$12$	$72$	$18$	$7.825$		None					140.2.k.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
980.2.x.m	$980$	$2$	980.x	140.w	$12$	$72$	$18$	$7.825$		None					140.2.w.b	$8$	$0$	\(2\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
980.2.x.n	$980$	$2$	980.x	140.w	$12$	$112$	$28$	$7.825$		None		✓	✓		980.2.k.m	$16$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(980, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)