Space of modular forms of level 21 and weight 4

• Label: 21.4
• Level: 21
• Weight: 4
• Dimension: 30
• Nonzero newspaces: 4
• Newform subspaces: 8
• Sturm bound: 128
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(21))\).

	Total	New	Old
Modular forms	60	42	18
Cusp forms	36	30	6
Eisenstein series	24	12	12

Trace form

30 * q + 3 * q^3 - 6 * q^4 - 24 * q^5 - 36 * q^6 - 54 * q^7 + 54 * q^8 + 39 * q^9 + 48 * q^10 - 96 * q^12 - 84 * q^13 - 312 * q^14 - 198 * q^15 - 126 * q^16 - 12 * q^17 + 270 * q^18 + 558 * q^19 + 1044 * q^20 + 585 * q^21 + 432 * q^22 - 168 * q^23 + 144 * q^24 - 426 * q^25 - 294 * q^26 - 108 * q^27 - 1110 * q^28 - 648 * q^29 - 1530 * q^30 - 750 * q^31 - 1218 * q^32 - 801 * q^33 - 276 * q^34 + 84 * q^35 + 258 * q^36 + 1422 * q^37 + 1710 * q^38 + 1212 * q^39 + 1416 * q^40 + 192 * q^41 + 2322 * q^42 + 1152 * q^43 + 2184 * q^44 + 2151 * q^45 + 708 * q^46 + 792 * q^47 - 1056 * q^48 - 2346 * q^49 - 3258 * q^50 - 3069 * q^51 - 4680 * q^52 - 2100 * q^53 - 4158 * q^54 - 1020 * q^55 + 690 * q^56 - 150 * q^57 + 3528 * q^58 - 336 * q^59 + 3060 * q^60 + 3138 * q^61 + 1812 * q^62 + 2283 * q^63 + 4278 * q^64 + 504 * q^65 + 882 * q^66 + 918 * q^67 - 1536 * q^68 - 1656 * q^69 - 3504 * q^70 - 492 * q^71 - 4050 * q^72 - 4326 * q^73 - 2730 * q^74 - 2304 * q^75 - 5544 * q^76 - 180 * q^77 + 504 * q^78 - 510 * q^79 + 3096 * q^80 + 3987 * q^81 + 7488 * q^82 + 4200 * q^83 + 7956 * q^84 + 4668 * q^85 + 5166 * q^86 + 1656 * q^87 - 1812 * q^88 - 1752 * q^89 - 1080 * q^90 + 804 * q^91 - 4704 * q^92 - 633 * q^93 + 504 * q^94 + 1344 * q^95 - 2700 * q^96 + 300 * q^97 - 5982 * q^98 - 4446 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.4.a	\(\chi_{21}(1, \cdot)\)	21.4.a.a	1	1
		21.4.a.b	1
		21.4.a.c	2
21.4.c	\(\chi_{21}(20, \cdot)\)	21.4.c.a	2	1
		21.4.c.b	4
21.4.e	\(\chi_{21}(4, \cdot)\)	21.4.e.a	2	2
		21.4.e.b	6
21.4.g	\(\chi_{21}(5, \cdot)\)	21.4.g.a	12	2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)