Space of modular forms of level 80, weight 10, and Character 80.l

• Label: 80.10.l
• Level: $80$
• Weight: $10$
• Character orbit: 80.l
• Rep. character: $\chi_{80}(21,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(80, [\chi])\).

	Total	New	Old
Modular forms	220	144	76
Cusp forms	212	144	68
Eisenstein series	8	0	8

Trace form

144 * q - 340 * q^4 + 4380 * q^6 - 22500 * q^10 - 131720 * q^11 - 202332 * q^12 + 158572 * q^14 - 405000 * q^15 + 1100304 * q^16 - 4357760 * q^18 + 480888 * q^19 + 905000 * q^20 - 1449020 * q^22 + 1160392 * q^24 + 6874256 * q^26 - 12650088 * q^27 - 6210484 * q^28 + 1266800 * q^29 + 28972800 * q^32 - 20791696 * q^34 - 8780244 * q^36 + 2429552 * q^37 + 33473660 * q^38 - 235316700 * q^42 - 38062456 * q^43 + 38038408 * q^44 - 16904684 * q^46 - 195187240 * q^47 - 13265320 * q^48 - 830131344 * q^49 + 26562500 * q^50 + 144699872 * q^51 - 236578536 * q^52 + 149815696 * q^53 - 136659488 * q^54 + 195461776 * q^56 + 64673132 * q^58 - 44969096 * q^59 + 376932500 * q^60 + 90121104 * q^61 - 45297368 * q^62 + 630118440 * q^63 + 690686960 * q^64 - 1231875840 * q^66 - 503547480 * q^67 - 199932912 * q^68 - 382360176 * q^69 + 362545000 * q^70 + 143491480 * q^72 + 35099016 * q^74 - 1132716032 * q^76 - 412088432 * q^77 + 1215379664 * q^78 - 1134564336 * q^79 - 1070390000 * q^80 - 6198727824 * q^81 - 353498868 * q^82 + 2478583720 * q^83 - 820902208 * q^84 - 429210000 * q^85 - 2353463468 * q^86 + 472599040 * q^88 - 1805602500 * q^90 - 2484604384 * q^91 + 2194605788 * q^92 - 2143933104 * q^93 + 918545012 * q^94 + 2606420000 * q^95 + 7242552840 * q^96 + 6931068612 * q^98 - 5099487112 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.10.l.a	$80$	$10$	80.l	16.e	$4$	$144$	$72$	$41.203$		None		✓	✓	✓	80.10.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{10}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)