Space of modular forms of level 2028 and weight 4

• Label: 2028.4
• Level: 2028
• Weight: 4
• Dimension: 146891
• Nonzero newspaces: 24
• Sturm bound: 908544
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(908544\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2028))\).

	Total	New	Old
Modular forms	342984	147711	195273
Cusp forms	338424	146891	191533
Eisenstein series	4560	820	3740

Trace form

146891 * q + 3 * q^3 - 140 * q^4 - 18 * q^5 - 90 * q^6 - 136 * q^7 - 135 * q^9 - 52 * q^10 + 276 * q^11 + 66 * q^12 + 90 * q^15 - 356 * q^16 + 390 * q^17 + 810 * q^18 - 244 * q^19 + 480 * q^20 - 468 * q^21 - 1452 * q^22 - 840 * q^23 - 1986 * q^24 - 1337 * q^25 - 1500 * q^26 - 1629 * q^27 - 2652 * q^28 - 1014 * q^29 - 786 * q^30 + 224 * q^31 + 2040 * q^32 + 696 * q^33 + 4700 * q^34 + 2976 * q^35 + 3018 * q^36 + 274 * q^37 - 492 * q^39 - 7708 * q^40 + 7878 * q^41 - 2310 * q^42 + 1796 * q^43 - 600 * q^44 + 582 * q^45 + 4236 * q^46 - 1056 * q^47 + 3198 * q^48 - 13091 * q^49 + 10584 * q^50 - 2394 * q^51 + 5364 * q^52 - 9906 * q^53 + 822 * q^54 - 6264 * q^55 + 6696 * q^56 - 4224 * q^57 + 236 * q^58 + 2004 * q^59 - 5046 * q^60 + 7906 * q^61 - 7080 * q^62 - 456 * q^63 - 13820 * q^64 + 11718 * q^65 - 13158 * q^66 + 8924 * q^67 + 5484 * q^69 - 2652 * q^70 + 696 * q^71 + 6306 * q^72 - 902 * q^73 + 2157 * q^75 + 2028 * q^76 - 12960 * q^77 + 8706 * q^78 - 10528 * q^79 - 1647 * q^81 - 1252 * q^82 + 1260 * q^83 + 1458 * q^84 + 3904 * q^85 - 19488 * q^86 + 3666 * q^87 - 19452 * q^88 + 2682 * q^89 - 24942 * q^90 + 4680 * q^91 - 4176 * q^92 - 4404 * q^93 + 1020 * q^94 + 8520 * q^95 + 930 * q^96 + 17938 * q^97 + 15768 * q^98 + 7164 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2028))\)

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
2028.4.a	\(\chi_{2028}(1, \cdot)\)	2028.4.a.a	1	1
		2028.4.a.b	1
		2028.4.a.c	1
		2028.4.a.d	2
		2028.4.a.e	2
		2028.4.a.f	2
		2028.4.a.g	2
		2028.4.a.h	2
		2028.4.a.i	2
		2028.4.a.j	4
		2028.4.a.k	4
		2028.4.a.l	4
		2028.4.a.m	4
		2028.4.a.n	4
		2028.4.a.o	6
		2028.4.a.p	9
		2028.4.a.q	9
		2028.4.a.r	9
		2028.4.a.s	9
2028.4.b	\(\chi_{2028}(337, \cdot)\)	2028.4.b.a	2	1
		2028.4.b.b	2
		2028.4.b.c	2
		2028.4.b.d	2
		2028.4.b.e	4
		2028.4.b.f	4
		2028.4.b.g	4
		2028.4.b.h	6
		2028.4.b.i	8
		2028.4.b.j	8
		2028.4.b.k	18
		2028.4.b.l	18
2028.4.c	\(\chi_{2028}(1691, \cdot)\)	n/a	908	1
2028.4.h	\(\chi_{2028}(2027, \cdot)\)	n/a	904	1
2028.4.i	\(\chi_{2028}(529, \cdot)\)	n/a	152	2
2028.4.k	\(\chi_{2028}(775, \cdot)\)	n/a	924	2
2028.4.m	\(\chi_{2028}(437, \cdot)\)	n/a	308	2
2028.4.p	\(\chi_{2028}(191, \cdot)\)	n/a	1808	2
2028.4.q	\(\chi_{2028}(361, \cdot)\)	n/a	156	2
2028.4.r	\(\chi_{2028}(23, \cdot)\)	n/a	1808	2
2028.4.u	\(\chi_{2028}(89, \cdot)\)	n/a	616	4
2028.4.w	\(\chi_{2028}(19, \cdot)\)	n/a	1848	4
2028.4.y	\(\chi_{2028}(157, \cdot)\)	n/a	1104	12
2028.4.z	\(\chi_{2028}(155, \cdot)\)	n/a	13056	12
2028.4.be	\(\chi_{2028}(131, \cdot)\)	n/a	13056	12
2028.4.bf	\(\chi_{2028}(25, \cdot)\)	n/a	1080	12
2028.4.bg	\(\chi_{2028}(61, \cdot)\)	n/a	2208	24
2028.4.bi	\(\chi_{2028}(5, \cdot)\)	n/a	4368	24
2028.4.bk	\(\chi_{2028}(31, \cdot)\)	n/a	13104	24
2028.4.bn	\(\chi_{2028}(95, \cdot)\)	n/a	26112	24
2028.4.bo	\(\chi_{2028}(49, \cdot)\)	n/a	2160	24
2028.4.bp	\(\chi_{2028}(35, \cdot)\)	n/a	26112	24
2028.4.bs	\(\chi_{2028}(7, \cdot)\)	n/a	26208	48
2028.4.bu	\(\chi_{2028}(41, \cdot)\)	n/a	8736	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2028))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2028)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 2}\)