Space of modular forms of level 980, weight 3, and Character 980.n

• Label: 980.3.n
• Level: $980$
• Weight: $3$
• Character orbit: 980.n
• Rep. character: $\chi_{980}(129,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $5$
• Sturm bound: $504$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	980.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(504\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(980, [\chi])\).

	Total	New	Old
Modular forms	720	80	640
Cusp forms	624	80	544
Eisenstein series	96	0	96

Trace form

80 * q - 3 * q^5 - 124 * q^9 + 6 * q^11 + 62 * q^15 + 48 * q^19 + 7 * q^25 - 180 * q^29 - 138 * q^31 - 62 * q^39 + 48 * q^45 + 248 * q^51 + 174 * q^59 + 390 * q^61 - 42 * q^65 + 88 * q^71 - 507 * q^75 - 208 * q^79 - 244 * q^81 + 502 * q^85 - 402 * q^89 - 313 * q^95 + 36 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(980, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
980.3.n.a	$980$	$3$	980.n	35.i	$6$	$4$	$2$	$26.703$	\(\Q(\sqrt{-3}, \sqrt{-35})\)	\(\Q(\sqrt{-35}) \)					140.3.h.a	$4$	$0$	\(0\)	\(-1\)	\(-10\)	\(0\)	$3$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{3}q^{3}+5\beta _{1}q^{5}+(17\beta _{1}+\beta _{2}-\beta _{3})q^{9}+\cdots\)
980.3.n.b	$980$	$3$	980.n	35.i	$6$	$4$	$2$	$26.703$	\(\Q(\sqrt{-3}, \sqrt{-35})\)	\(\Q(\sqrt{-35}) \)					140.3.h.a	$4$	$0$	\(0\)	\(1\)	\(10\)	\(0\)	$3$	$\mathrm{U}(1)[D_{6}]$	\(q+(1+\beta _{1}+\beta _{3})q^{3}-5\beta _{1}q^{5}+(18\beta _{1}+\cdots)q^{9}+\cdots\)
980.3.n.c	$980$	$3$	980.n	35.i	$6$	$8$	$4$	$26.703$	8.0.\(\cdots\).6	None					140.3.h.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{3}+(-\beta _{1}-2\beta _{4})q^{5}+7\beta _{2}q^{9}+\cdots\)
980.3.n.d	$980$	$3$	980.n	35.i	$6$	$16$	$8$	$26.703$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					140.3.n.a	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}-\beta _{10}q^{5}+(-2+2\beta _{3}+\beta _{8}+\cdots)q^{9}+\cdots\)
980.3.n.e	$980$	$3$	980.n	35.i	$6$	$48$	$24$	$26.703$		None		✓	✓		980.3.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

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