Space of modular forms of level 180 and weight 8

• Label: 180.8
• Level: 180
• Weight: 8
• Dimension: 2535
• Nonzero newspaces: 12
• Sturm bound: 13824
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(13824\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(180))\).

	Total	New	Old
Modular forms	6208	2591	3617
Cusp forms	5888	2535	3353
Eisenstein series	320	56	264

Trace form

2535 * q + 102 * q^4 - 466 * q^5 - 442 * q^6 + 1576 * q^7 - 1008 * q^8 - 2616 * q^9 - 6258 * q^10 + 4558 * q^11 + 37636 * q^12 + 9062 * q^13 - 86976 * q^14 - 17313 * q^15 - 38750 * q^16 + 4936 * q^17 + 143768 * q^18 + 4412 * q^19 - 172126 * q^20 - 56618 * q^21 + 304262 * q^22 + 3528 * q^23 + 290742 * q^24 + 1272096 * q^25 - 331604 * q^26 - 214728 * q^27 - 11864 * q^28 + 327948 * q^29 + 1238394 * q^30 + 381558 * q^31 - 17770 * q^32 - 333450 * q^33 - 1159998 * q^34 + 349528 * q^35 - 1077678 * q^36 + 2033016 * q^37 + 3921550 * q^38 - 1109018 * q^39 - 1172930 * q^40 - 6216892 * q^41 + 793468 * q^42 + 721364 * q^43 + 3264621 * q^45 + 5963672 * q^46 + 1599540 * q^47 + 105470 * q^48 + 2613789 * q^49 - 754816 * q^50 - 3803808 * q^51 - 3967312 * q^52 - 14400128 * q^53 + 3022958 * q^54 + 1544526 * q^55 + 8215076 * q^56 + 11872520 * q^57 + 6607024 * q^58 - 1557614 * q^59 - 15086006 * q^60 - 5771828 * q^61 - 3866228 * q^62 - 13919974 * q^63 - 20735172 * q^64 - 8868289 * q^65 + 23377684 * q^66 - 973100 * q^67 + 3870542 * q^68 - 1920374 * q^69 + 4988232 * q^70 + 21681540 * q^71 - 2639526 * q^72 + 26947840 * q^73 - 26491620 * q^74 - 47201799 * q^75 - 20717058 * q^76 - 35408178 * q^77 - 18184504 * q^78 - 18305386 * q^79 + 56330512 * q^80 + 39876972 * q^81 + 57761196 * q^82 + 39162132 * q^83 + 30728644 * q^84 - 36529246 * q^85 - 54272690 * q^86 + 2903050 * q^87 - 52176346 * q^88 - 35926618 * q^89 - 88883934 * q^90 + 23793040 * q^91 - 84017872 * q^92 + 116510518 * q^93 + 51576972 * q^94 + 58625232 * q^95 + 141318680 * q^96 - 74085630 * q^97 + 144120270 * q^98 - 54650714 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(180))\)

We only show spaces with even 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
180.8.a	\(\chi_{180}(1, \cdot)\)	180.8.a.a	1	1
		180.8.a.b	1
		180.8.a.c	1
		180.8.a.d	1
		180.8.a.e	1
		180.8.a.f	2
		180.8.a.g	2
		180.8.a.h	2
180.8.d	\(\chi_{180}(109, \cdot)\)	180.8.d.a	2	1
		180.8.d.b	4
		180.8.d.c	4
		180.8.d.d	8
180.8.e	\(\chi_{180}(71, \cdot)\)	180.8.e.a	56	1
180.8.h	\(\chi_{180}(179, \cdot)\)	180.8.h.a	4	1
		180.8.h.b	80
180.8.i	\(\chi_{180}(61, \cdot)\)	180.8.i.a	26	2
		180.8.i.b	30
180.8.j	\(\chi_{180}(17, \cdot)\)	180.8.j.a	28	2
180.8.k	\(\chi_{180}(127, \cdot)\)	n/a	206	2
180.8.n	\(\chi_{180}(59, \cdot)\)	n/a	496	2
180.8.q	\(\chi_{180}(11, \cdot)\)	n/a	336	2
180.8.r	\(\chi_{180}(49, \cdot)\)	180.8.r.a	84	2
180.8.w	\(\chi_{180}(77, \cdot)\)	n/a	168	4
180.8.x	\(\chi_{180}(7, \cdot)\)	n/a	992	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(180))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(180)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)