Space of modular forms of level 80 and weight 11

• Label: 80.11
• Level: 80
• Weight: 11
• Dimension: 976
• Nonzero newspaces: 7
• Newform subspaces: 16
• Sturm bound: 4224
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(4224\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	1976	1004	972
Cusp forms	1864	976	888
Eisenstein series	112	28	84

Trace form

976 * q - 4 * q^2 - 2 * q^3 + 2504 * q^4 - 4682 * q^5 + 34416 * q^6 + 2 * q^7 - 138256 * q^8 + 260454 * q^9 + 147356 * q^10 + 91800 * q^11 + 21968 * q^12 + 424526 * q^13 - 1515680 * q^14 - 2076438 * q^15 + 938048 * q^16 + 6217842 * q^17 - 4133860 * q^18 + 10214076 * q^19 - 5301524 * q^20 - 967692 * q^21 + 41137840 * q^22 + 32805522 * q^23 - 117039464 * q^24 + 15602324 * q^25 + 36903008 * q^26 + 20641864 * q^27 + 64530952 * q^28 + 137461984 * q^29 - 79150188 * q^30 - 58368332 * q^31 - 8916784 * q^32 + 114045668 * q^33 + 393352592 * q^34 + 19531246 * q^35 - 352590824 * q^36 + 38423430 * q^37 - 836154624 * q^38 + 559683448 * q^39 + 1049644192 * q^40 - 173740536 * q^41 + 981566200 * q^42 - 329069666 * q^43 - 1141578584 * q^44 - 13498172 * q^45 - 845613704 * q^46 - 809409366 * q^47 + 940631656 * q^48 - 1670510206 * q^49 + 2470875696 * q^50 - 691460772 * q^51 - 2247374064 * q^52 + 298666134 * q^53 - 1343571528 * q^54 + 2122360528 * q^55 + 2771246912 * q^56 - 4495330672 * q^57 - 75123448 * q^58 - 3087367716 * q^59 - 310481000 * q^60 + 1538636460 * q^61 + 1966125976 * q^62 - 5429343982 * q^63 - 1976708896 * q^64 - 1352293898 * q^65 + 925330024 * q^66 + 305290734 * q^67 + 12991108992 * q^68 + 8846241536 * q^69 - 4644201184 * q^70 - 3514702884 * q^71 - 40684174888 * q^72 - 9746476318 * q^73 - 480355496 * q^74 - 10822302230 * q^75 + 23159721576 * q^76 + 5504363596 * q^77 - 1778526824 * q^78 - 2460042560 * q^80 + 25787013256 * q^81 - 38515923352 * q^82 - 7235083250 * q^83 - 23396223440 * q^84 + 12547832206 * q^85 + 31390199144 * q^86 - 5069347664 * q^87 + 52006006256 * q^88 - 336850716 * q^89 - 9904045768 * q^90 - 38402200900 * q^91 - 117882973792 * q^92 - 7842097356 * q^93 - 7016063696 * q^94 + 290617000 * q^95 + 47251696720 * q^96 + 50400627594 * q^97 + 61651844724 * q^98 + 79127043396 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(80))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
80.11.b	\(\chi_{80}(31, \cdot)\)	80.11.b.a	8	1
		80.11.b.b	12
80.11.e	\(\chi_{80}(39, \cdot)\)	None	0	1
80.11.g	\(\chi_{80}(71, \cdot)\)	None	0	1
80.11.h	\(\chi_{80}(79, \cdot)\)	80.11.h.a	2	1
		80.11.h.b	8
		80.11.h.c	20
80.11.i	\(\chi_{80}(13, \cdot)\)	80.11.i.a	236	2
80.11.k	\(\chi_{80}(19, \cdot)\)	80.11.k.a	236	2
80.11.m	\(\chi_{80}(57, \cdot)\)	None	0	2
80.11.p	\(\chi_{80}(17, \cdot)\)	80.11.p.a	2	2
		80.11.p.b	2
		80.11.p.c	6
		80.11.p.d	8
		80.11.p.e	10
		80.11.p.f	14
		80.11.p.g	16
80.11.r	\(\chi_{80}(11, \cdot)\)	80.11.r.a	160	2
80.11.t	\(\chi_{80}(53, \cdot)\)	80.11.t.a	236	2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)