Space of modular forms of level 21 and weight 8

• Label: 21.8
• Level: 21
• Weight: 8
• Dimension: 76
• Nonzero newspaces: 4
• Newform subspaces: 9
• Sturm bound: 256
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(256\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(21))\).

	Total	New	Old
Modular forms	124	88	36
Cusp forms	100	76	24
Eisenstein series	24	12	12

Trace form

76 * q - 12 * q^2 + 24 * q^3 + 690 * q^4 - 774 * q^5 - 972 * q^6 - 606 * q^7 + 6294 * q^8 - 2994 * q^9 + 13488 * q^10 - 606 * q^11 - 26112 * q^12 + 1978 * q^13 - 38904 * q^14 + 36972 * q^15 + 88498 * q^16 + 5232 * q^17 + 16578 * q^18 - 8618 * q^19 - 390876 * q^20 - 22668 * q^21 + 482016 * q^22 + 349128 * q^23 - 133632 * q^24 - 243506 * q^25 - 688230 * q^26 - 39366 * q^27 - 537878 * q^28 + 93048 * q^29 + 510390 * q^30 + 1537126 * q^31 + 324750 * q^32 + 460638 * q^33 - 922524 * q^34 - 1268766 * q^35 - 924438 * q^36 - 1910076 * q^37 - 318858 * q^38 + 1448346 * q^39 + 3743976 * q^40 + 2477124 * q^41 + 4004046 * q^42 + 671520 * q^43 - 4494888 * q^44 - 5321754 * q^45 - 3647964 * q^46 + 834846 * q^47 - 2224800 * q^48 + 2965030 * q^49 + 397122 * q^50 + 7116084 * q^51 + 3677944 * q^52 - 757140 * q^53 - 6507702 * q^54 - 808440 * q^55 - 5485998 * q^56 - 9009756 * q^57 - 16780824 * q^58 - 4170036 * q^59 + 6846660 * q^60 + 20004946 * q^61 + 29624580 * q^62 + 10650138 * q^63 + 19885062 * q^64 + 2724594 * q^65 - 10102230 * q^66 - 24006694 * q^67 - 17104800 * q^68 - 8709768 * q^69 - 31565424 * q^70 - 1570548 * q^71 + 6811614 * q^72 + 3188920 * q^73 + 9720006 * q^74 - 7245654 * q^75 - 204728 * q^76 - 497568 * q^77 - 5336928 * q^78 + 16708382 * q^79 + 39324216 * q^80 + 17986770 * q^81 - 15181704 * q^82 - 12957732 * q^83 + 22358892 * q^84 - 22609392 * q^85 + 27742854 * q^86 + 26620524 * q^87 + 17131884 * q^88 + 13223256 * q^89 - 12159720 * q^90 - 23810888 * q^91 - 10696896 * q^92 - 51166212 * q^93 - 44319000 * q^94 - 44732166 * q^95 - 68479020 * q^96 - 17004164 * q^97 - 55932810 * q^98 + 18079740 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.8.a	\(\chi_{21}(1, \cdot)\)	21.8.a.a	1	1
		21.8.a.b	2
		21.8.a.c	2
		21.8.a.d	3
21.8.c	\(\chi_{21}(20, \cdot)\)	21.8.c.a	16	1
21.8.e	\(\chi_{21}(4, \cdot)\)	21.8.e.a	8	2
		21.8.e.b	10
21.8.g	\(\chi_{21}(5, \cdot)\)	21.8.g.a	2	2
		21.8.g.b	32

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)