Space of modular forms of level 1980, weight 4, and Character 1980.c

• Label: 1980.4.c
• Level: $1980$
• Weight: $4$
• Character orbit: 1980.c
• Rep. character: $\chi_{1980}(1189,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $7$
• Sturm bound: $1728$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1980.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1728\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1980, [\chi])\).

	Total	New	Old
Modular forms	1320	74	1246
Cusp forms	1272	74	1198
Eisenstein series	48	0	48

Trace form

74 * q - 8 * q^5 + 22 * q^11 - 144 * q^19 + 20 * q^25 - 220 * q^29 - 196 * q^31 - 568 * q^35 + 588 * q^41 - 3182 * q^49 + 198 * q^55 - 1536 * q^59 - 1860 * q^61 - 1984 * q^65 + 3308 * q^71 + 2688 * q^79 + 3068 * q^85 - 548 * q^89 - 5128 * q^91 - 4032 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(1980, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1980.4.c.a	$1980$	$4$	1980.c	5.b	$2$	$2$	$2$	$116.824$	\(\Q(\sqrt{-19}) \)	None					220.4.b.a	$2$	$0$	\(0\)	\(0\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(5-5\beta )q^{5}+(2-4\beta )q^{7}+11q^{11}+\cdots\)
1980.4.c.b	$1980$	$4$	1980.c	5.b	$2$	$6$	$6$	$116.824$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					220.4.b.c	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{4})q^{5}+(-3\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
1980.4.c.c	$1980$	$4$	1980.c	5.b	$2$	$6$	$6$	$116.824$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					220.4.b.b	$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta _{1}-\beta _{4})q^{5}-\beta _{3}q^{7}+11q^{11}+\cdots\)
1980.4.c.d	$1980$	$4$	1980.c	5.b	$2$	$14$	$14$	$116.824$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			1980.4.c.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{5}+\beta _{4}q^{7}-11q^{11}+(\beta _{3}+\beta _{4}+\cdots)q^{13}+\cdots\)
1980.4.c.e	$1980$	$4$	1980.c	5.b	$2$	$14$	$14$	$116.824$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			1980.4.c.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}+\beta _{4}q^{7}+11q^{11}+(\beta _{3}+\beta _{4}+\cdots)q^{13}+\cdots\)
1980.4.c.f	$1980$	$4$	1980.c	5.b	$2$	$16$	$16$	$116.824$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					660.4.c.b	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{23}\cdot 3^{8}\cdot 5\cdot 17^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{5}+\beta _{1}q^{7}-11q^{11}+\cdots\)
1980.4.c.g	$1980$	$4$	1980.c	5.b	$2$	$16$	$16$	$116.824$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					660.4.c.a	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{24}\cdot 3^{8}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2})q^{5}+\beta _{6}q^{7}+11q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1980, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1980, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 2}\)