Space of modular forms of level 21 and weight 3

• Label: 21.3
• Level: 21
• Weight: 3
• Dimension: 18
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 96
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(21))\).

	Total	New	Old
Modular forms	44	26	18
Cusp forms	20	18	2
Eisenstein series	24	8	16

Trace form

18 * q - 6 * q^3 - 22 * q^4 - 6 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 - 24 * q^9 - 12 * q^10 + 6 * q^11 + 18 * q^12 + 2 * q^13 + 24 * q^14 + 48 * q^15 + 90 * q^16 + 48 * q^17 + 96 * q^18 + 2 * q^19 - 24 * q^21 - 108 * q^22 - 96 * q^23 - 150 * q^24 - 132 * q^25 - 126 * q^26 - 132 * q^27 - 102 * q^28 - 12 * q^29 + 24 * q^30 + 86 * q^31 + 78 * q^32 + 186 * q^33 + 240 * q^34 + 210 * q^35 + 198 * q^36 + 160 * q^37 + 174 * q^38 + 66 * q^39 + 96 * q^40 - 72 * q^42 - 188 * q^43 - 168 * q^44 - 198 * q^45 - 204 * q^46 - 222 * q^47 - 210 * q^48 - 120 * q^49 - 114 * q^50 - 168 * q^51 + 152 * q^52 - 12 * q^53 - 84 * q^54 + 156 * q^55 + 18 * q^56 + 108 * q^57 + 84 * q^59 + 96 * q^60 + 38 * q^61 + 78 * q^63 - 34 * q^64 + 18 * q^65 - 36 * q^66 + 102 * q^67 + 36 * q^68 + 288 * q^69 - 60 * q^70 + 120 * q^71 + 174 * q^72 - 100 * q^73 + 90 * q^74 + 180 * q^75 - 292 * q^76 + 72 * q^77 + 24 * q^78 + 162 * q^79 + 48 * q^80 + 108 * q^82 + 102 * q^84 - 168 * q^85 + 210 * q^86 + 12 * q^87 - 24 * q^88 - 60 * q^89 - 132 * q^90 - 148 * q^91 - 84 * q^92 - 264 * q^93 - 324 * q^94 - 438 * q^95 - 402 * q^96 - 376 * q^97 - 270 * q^98 - 432 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)

We only show spaces with odd 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
21.3.b	\(\chi_{21}(8, \cdot)\)	21.3.b.a	4	1
21.3.d	\(\chi_{21}(13, \cdot)\)	21.3.d.a	2	1
21.3.f	\(\chi_{21}(10, \cdot)\)	21.3.f.a	2	2
		21.3.f.b	2
		21.3.f.c	2
21.3.h	\(\chi_{21}(2, \cdot)\)	21.3.h.a	2	2
		21.3.h.b	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

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