Space of modular forms of level 180 and weight 4

• Label: 180.4
• Level: 180
• Weight: 4
• Dimension: 1071
• Nonzero newspaces: 12
• Newform subspaces: 28
• Sturm bound: 6912
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(6912\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(180))\).

	Total	New	Old
Modular forms	2752	1127	1625
Cusp forms	2432	1071	1361
Eisenstein series	320	56	264

Trace form

1071 * q + 6 * q^3 - 26 * q^4 - 11 * q^5 - 58 * q^6 - 20 * q^7 - 48 * q^8 - 42 * q^9 + 62 * q^10 - 82 * q^11 + 4 * q^12 - 216 * q^13 + 144 * q^14 + 12 * q^15 - 350 * q^16 + 164 * q^17 + 200 * q^18 + 112 * q^19 + 34 * q^20 + 340 * q^21 + 422 * q^22 - 180 * q^23 - 42 * q^24 + 1281 * q^25 + 620 * q^26 - 744 * q^27 + 136 * q^28 - 342 * q^29 + 714 * q^30 + 528 * q^31 - 170 * q^32 + 1686 * q^33 + 594 * q^34 + 128 * q^35 - 2478 * q^36 - 640 * q^37 - 2530 * q^38 - 344 * q^39 - 1010 * q^40 - 1448 * q^41 - 2228 * q^42 - 1934 * q^43 - 444 * q^45 - 552 * q^46 - 804 * q^47 + 4670 * q^48 + 1791 * q^49 + 1864 * q^50 + 3150 * q^51 + 3408 * q^52 + 5384 * q^53 + 4526 * q^54 + 3676 * q^55 + 2788 * q^56 + 326 * q^57 - 2656 * q^58 + 914 * q^59 - 2246 * q^60 + 3054 * q^61 - 3988 * q^62 - 1504 * q^63 - 2756 * q^64 - 464 * q^65 - 7196 * q^66 - 1754 * q^67 - 10514 * q^68 - 3008 * q^69 - 3408 * q^70 - 7272 * q^71 - 2982 * q^72 - 3872 * q^73 + 924 * q^74 + 1446 * q^75 + 1470 * q^76 - 7260 * q^77 + 392 * q^78 - 4328 * q^79 + 3152 * q^80 - 6066 * q^81 + 1388 * q^82 - 2196 * q^83 + 2980 * q^84 + 5264 * q^85 + 8558 * q^86 + 196 * q^87 + 9254 * q^88 + 3130 * q^89 - 2334 * q^90 + 10016 * q^91 + 9808 * q^92 - 2216 * q^93 + 11900 * q^94 - 228 * q^95 + 1016 * q^96 + 6858 * q^97 + 1710 * q^98 + 1420 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(180))\)

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
180.4.a	\(\chi_{180}(1, \cdot)\)	180.4.a.a	1	1
		180.4.a.b	1
		180.4.a.c	1
		180.4.a.d	1
		180.4.a.e	1
180.4.d	\(\chi_{180}(109, \cdot)\)	180.4.d.a	2	1
		180.4.d.b	2
		180.4.d.c	4
180.4.e	\(\chi_{180}(71, \cdot)\)	180.4.e.a	24	1
180.4.h	\(\chi_{180}(179, \cdot)\)	180.4.h.a	4	1
		180.4.h.b	32
180.4.i	\(\chi_{180}(61, \cdot)\)	180.4.i.a	2	2
		180.4.i.b	8
		180.4.i.c	14
180.4.j	\(\chi_{180}(17, \cdot)\)	180.4.j.a	12	2
180.4.k	\(\chi_{180}(127, \cdot)\)	180.4.k.a	2	2
		180.4.k.b	2
		180.4.k.c	2
		180.4.k.d	8
		180.4.k.e	12
		180.4.k.f	28
		180.4.k.g	32
180.4.n	\(\chi_{180}(59, \cdot)\)	180.4.n.a	8	2
		180.4.n.b	200
180.4.q	\(\chi_{180}(11, \cdot)\)	180.4.q.a	144	2
180.4.r	\(\chi_{180}(49, \cdot)\)	180.4.r.a	36	2
180.4.w	\(\chi_{180}(77, \cdot)\)	180.4.w.a	72	4
180.4.x	\(\chi_{180}(7, \cdot)\)	180.4.x.a	416	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(180))\) into lower level spaces

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