Space of modular forms of level 80, weight 18, and Character 80.c

• Label: 80.18.c
• Level: $80$
• Weight: $18$
• Character orbit: 80.c
• Rep. character: $\chi_{80}(49,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $4$
• Sturm bound: $216$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(216\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(80, [\chi])\).

	Total	New	Old
Modular forms	210	52	158
Cusp forms	198	50	148
Eisenstein series	12	2	10

Trace form

50 * q + 12238 * q^5 - 2066242610 * q^9 + 1286153288 * q^11 + 17470096312 * q^15 - 83017221192 * q^19 - 127848609208 * q^21 + 609106039274 * q^25 + 2457618148892 * q^29 - 2718162991616 * q^31 + 30651535433288 * q^35 + 92825949991568 * q^39 - 51479687678492 * q^41 - 3397054404558 * q^45 - 1290938162405866 * q^49 + 957769831296512 * q^51 + 30163371244472 * q^55 - 2360427133472472 * q^59 - 927794765960948 * q^61 + 1500981275740816 * q^65 + 5315253814103112 * q^69 - 18948979179237520 * q^71 - 32086568148399984 * q^75 - 26681025923779808 * q^79 + 109841046032690522 * q^81 + 2434376811978240 * q^85 + 59866059152801748 * q^89 + 22598302209669488 * q^91 + 17352761544037448 * q^95 - 172230294252876872 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.18.c.a	$80$	$18$	80.c	5.b	$2$	$8$	$8$	$146.578$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					10.18.b.a	$2$	$0$	\(0\)	\(0\)	\(-1225560\)	\(0\)	$2^{42}\cdot 3^{4}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-153195+54\beta _{1}+28\beta _{2}+\cdots)q^{5}+\cdots\)
80.18.c.b	$80$	$18$	80.c	5.b	$2$	$8$	$8$	$146.578$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					5.18.b.a	$2$	$0$	\(0\)	\(0\)	\(379200\)	\(0\)	$2^{35}\cdot 3^{8}\cdot 5^{12}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(47400-2\beta _{1}+24\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
80.18.c.c	$80$	$18$	80.c	5.b	$2$	$8$	$8$	$146.578$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					20.18.c.a	$2$	$0$	\(0\)	\(0\)	\(1276800\)	\(0\)	$2^{35}\cdot 3^{4}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(159600+4\beta _{1}+\beta _{2})q^{5}+\cdots\)
80.18.c.d	$80$	$18$	80.c	5.b	$2$	$26$	$26$	$146.578$		None			✓		40.18.c.a	$2$	$0$	\(0\)	\(0\)	\(-418202\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{18}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{18}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{18}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)