Space of modular forms of level 2028 and weight 2

• Label: 2028.2
• Level: 2028
• Weight: 2
• Dimension: 48690
• Nonzero newspaces: 24
• Sturm bound: 454272
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(454272\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2028))\).

	Total	New	Old
Modular forms	115848	49510	66338
Cusp forms	111289	48690	62599
Eisenstein series	4559	820	3739

Trace form

48690 * q - 132 * q^4 - 66 * q^6 - 8 * q^7 - 136 * q^9 - 132 * q^10 - 24 * q^11 - 54 * q^12 - 312 * q^13 - 24 * q^15 - 132 * q^16 - 12 * q^17 - 30 * q^18 + 16 * q^19 + 96 * q^20 - 88 * q^21 - 12 * q^22 + 48 * q^23 + 30 * q^24 - 156 * q^25 + 60 * q^26 + 72 * q^27 - 12 * q^28 + 60 * q^29 + 30 * q^30 + 48 * q^31 + 120 * q^32 - 48 * q^33 - 36 * q^34 + 48 * q^35 - 30 * q^36 - 252 * q^37 + 28 * q^39 - 348 * q^40 + 132 * q^41 - 102 * q^42 + 64 * q^43 - 120 * q^44 - 36 * q^45 - 372 * q^46 + 48 * q^47 - 162 * q^48 + 40 * q^49 - 216 * q^50 + 48 * q^51 - 252 * q^52 + 96 * q^53 - 42 * q^54 + 24 * q^55 - 216 * q^56 - 40 * q^57 - 324 * q^58 - 24 * q^59 - 246 * q^60 - 132 * q^61 - 120 * q^62 - 124 * q^63 - 252 * q^64 + 18 * q^65 - 294 * q^66 - 80 * q^67 - 288 * q^69 - 252 * q^70 - 48 * q^71 - 222 * q^72 - 344 * q^73 - 208 * q^75 - 132 * q^76 - 144 * q^77 - 186 * q^78 - 144 * q^79 - 256 * q^81 - 132 * q^82 - 72 * q^83 - 318 * q^84 - 420 * q^85 - 96 * q^86 - 168 * q^87 - 252 * q^88 - 144 * q^89 - 366 * q^90 - 52 * q^91 - 144 * q^92 - 304 * q^93 - 324 * q^94 - 96 * q^95 - 318 * q^96 - 432 * q^97 - 216 * q^98 + 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2028))\)

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
2028.2.a	\(\chi_{2028}(1, \cdot)\)	2028.2.a.a	1	1
		2028.2.a.b	1
		2028.2.a.c	1
		2028.2.a.d	1
		2028.2.a.e	1
		2028.2.a.f	1
		2028.2.a.g	2
		2028.2.a.h	2
		2028.2.a.i	3
		2028.2.a.j	3
		2028.2.a.k	3
		2028.2.a.l	3
		2028.2.a.m	4
2028.2.b	\(\chi_{2028}(337, \cdot)\)	2028.2.b.a	2	1
		2028.2.b.b	2
		2028.2.b.c	2
		2028.2.b.d	2
		2028.2.b.e	4
		2028.2.b.f	6
		2028.2.b.g	6
2028.2.c	\(\chi_{2028}(1691, \cdot)\)	n/a	288	1
2028.2.h	\(\chi_{2028}(2027, \cdot)\)	n/a	288	1
2028.2.i	\(\chi_{2028}(529, \cdot)\)	2028.2.i.a	2	2
		2028.2.i.b	2
		2028.2.i.c	2
		2028.2.i.d	2
		2028.2.i.e	2
		2028.2.i.f	2
		2028.2.i.g	2
		2028.2.i.h	4
		2028.2.i.i	4
		2028.2.i.j	6
		2028.2.i.k	6
		2028.2.i.l	6
		2028.2.i.m	6
		2028.2.i.n	8
2028.2.k	\(\chi_{2028}(775, \cdot)\)	n/a	308	2
2028.2.m	\(\chi_{2028}(437, \cdot)\)	n/a	104	2
2028.2.p	\(\chi_{2028}(191, \cdot)\)	n/a	576	2
2028.2.q	\(\chi_{2028}(361, \cdot)\)	2028.2.q.a	2	2
		2028.2.q.b	2
		2028.2.q.c	2
		2028.2.q.d	4
		2028.2.q.e	4
		2028.2.q.f	4
		2028.2.q.g	4
		2028.2.q.h	4
		2028.2.q.i	12
		2028.2.q.j	12
2028.2.r	\(\chi_{2028}(23, \cdot)\)	n/a	576	2
2028.2.u	\(\chi_{2028}(89, \cdot)\)	n/a	204	4
2028.2.w	\(\chi_{2028}(19, \cdot)\)	n/a	616	4
2028.2.y	\(\chi_{2028}(157, \cdot)\)	n/a	360	12
2028.2.z	\(\chi_{2028}(155, \cdot)\)	n/a	4320	12
2028.2.be	\(\chi_{2028}(131, \cdot)\)	n/a	4320	12
2028.2.bf	\(\chi_{2028}(25, \cdot)\)	n/a	384	12
2028.2.bg	\(\chi_{2028}(61, \cdot)\)	n/a	696	24
2028.2.bi	\(\chi_{2028}(5, \cdot)\)	n/a	1440	24
2028.2.bk	\(\chi_{2028}(31, \cdot)\)	n/a	4368	24
2028.2.bn	\(\chi_{2028}(95, \cdot)\)	n/a	8640	24
2028.2.bo	\(\chi_{2028}(49, \cdot)\)	n/a	744	24
2028.2.bp	\(\chi_{2028}(35, \cdot)\)	n/a	8640	24
2028.2.bs	\(\chi_{2028}(7, \cdot)\)	n/a	8736	48
2028.2.bu	\(\chi_{2028}(41, \cdot)\)	n/a	2928	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2028))\) into lower level spaces

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