Space of modular forms of level 21 and weight 6

• Label: 21.6
• Level: 21
• Weight: 6
• Dimension: 52
• Nonzero newspaces: 4
• Newform subspaces: 11
• Sturm bound: 192
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(21))\).

	Total	New	Old
Modular forms	92	64	28
Cusp forms	68	52	16
Eisenstein series	24	12	12

Trace form

52 * q + 12 * q^2 - 12 * q^3 - 142 * q^4 + 54 * q^5 + 324 * q^6 + 266 * q^7 + 6 * q^8 - 816 * q^9 - 3024 * q^10 + 714 * q^11 + 2040 * q^12 + 2070 * q^13 + 3480 * q^14 + 2268 * q^15 + 178 * q^16 - 5016 * q^17 - 6534 * q^18 + 2838 * q^19 - 5052 * q^20 - 5334 * q^21 - 12816 * q^22 - 5976 * q^23 + 6696 * q^24 + 25114 * q^25 + 22986 * q^26 + 1458 * q^27 + 11146 * q^28 - 5568 * q^29 - 21042 * q^30 - 15018 * q^31 - 1794 * q^32 + 17604 * q^33 - 13548 * q^34 - 13158 * q^35 + 64410 * q^36 + 38944 * q^37 + 32118 * q^38 - 29814 * q^39 - 106152 * q^40 - 32940 * q^41 - 90306 * q^42 - 16688 * q^43 - 8424 * q^44 - 22104 * q^45 + 7524 * q^46 + 5934 * q^47 + 71136 * q^48 - 8006 * q^49 + 28650 * q^50 + 72072 * q^51 + 165528 * q^52 + 4812 * q^53 + 123282 * q^54 + 229272 * q^55 + 84018 * q^56 + 43488 * q^57 - 138552 * q^58 - 61188 * q^59 - 257796 * q^60 - 263238 * q^61 - 117756 * q^62 - 188958 * q^63 - 339994 * q^64 - 233682 * q^65 - 303534 * q^66 + 24986 * q^67 + 89904 * q^68 + 129384 * q^69 + 730224 * q^70 + 310188 * q^71 + 603126 * q^72 + 412644 * q^73 + 288102 * q^74 + 431706 * q^75 + 131400 * q^76 - 173184 * q^77 - 246816 * q^78 - 641170 * q^79 - 244056 * q^80 - 109764 * q^81 - 656424 * q^82 - 437652 * q^83 - 795156 * q^84 - 363240 * q^85 - 95322 * q^86 - 437076 * q^87 + 52140 * q^88 + 146496 * q^89 + 103032 * q^90 + 283224 * q^91 + 872928 * q^92 + 1050546 * q^93 + 1055448 * q^94 + 722922 * q^95 + 1080036 * q^96 - 366516 * q^97 - 16626 * q^98 + 500868 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.6.a	\(\chi_{21}(1, \cdot)\)	21.6.a.a	1	1
		21.6.a.b	1
		21.6.a.c	1
		21.6.a.d	1
21.6.c	\(\chi_{21}(20, \cdot)\)	21.6.c.a	12	1
21.6.e	\(\chi_{21}(4, \cdot)\)	21.6.e.a	2	2
		21.6.e.b	4
		21.6.e.c	8
21.6.g	\(\chi_{21}(5, \cdot)\)	21.6.g.a	2	2
		21.6.g.b	4
		21.6.g.c	16

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)