Space of modular forms of level 21 and weight 10

• Label: 21.10
• Level: 21
• Weight: 10
• Dimension: 98
• Nonzero newspaces: 4
• Newform subspaces: 9
• Sturm bound: 320
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(320\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(21))\).

	Total	New	Old
Modular forms	156	110	46
Cusp forms	132	98	34
Eisenstein series	24	12	12

Trace form

98 * q + 36 * q^2 - 165 * q^3 - 1198 * q^4 + 3984 * q^5 - 972 * q^6 - 7390 * q^7 - 57114 * q^8 + 24447 * q^9 + 60816 * q^10 - 193392 * q^11 + 73032 * q^12 + 777964 * q^13 + 6072 * q^14 - 804582 * q^15 - 1249678 * q^16 + 166116 * q^17 + 2531682 * q^18 - 975026 * q^19 - 677052 * q^20 - 1902687 * q^21 + 4851696 * q^22 - 40584 * q^23 + 622872 * q^24 - 8024206 * q^25 - 5592630 * q^26 + 2125764 * q^27 + 36460490 * q^28 - 1442304 * q^29 - 18021042 * q^30 - 53538302 * q^31 - 42431010 * q^32 - 565533 * q^33 + 103018020 * q^34 + 72736692 * q^35 + 100034394 * q^36 - 99897170 * q^37 - 114008058 * q^38 - 34117188 * q^39 + 38176248 * q^40 + 61439352 * q^41 + 3310326 * q^42 - 49446032 * q^43 - 232746792 * q^44 + 105366411 * q^45 + 98011332 * q^46 + 133604856 * q^47 + 130012128 * q^48 + 42288938 * q^49 - 221439150 * q^50 - 265707405 * q^51 - 347503400 * q^52 - 196886868 * q^53 + 410463666 * q^54 + 509470932 * q^55 + 85364850 * q^56 + 421245450 * q^57 + 352123464 * q^58 + 291494352 * q^59 - 615514356 * q^60 - 533295350 * q^61 - 1137678492 * q^62 - 550876773 * q^63 - 465830938 * q^64 + 459625608 * q^65 + 1379156994 * q^66 + 777988870 * q^67 + 472762896 * q^68 + 672641496 * q^69 + 540777744 * q^70 + 131491572 * q^71 - 1834381242 * q^72 - 431625614 * q^73 - 2578991514 * q^74 - 347823384 * q^75 - 1301542904 * q^76 + 63994212 * q^77 + 4145078160 * q^78 + 2627235058 * q^79 + 3089728584 * q^80 - 3059671221 * q^81 - 2139679800 * q^82 + 227089704 * q^83 - 5060061492 * q^84 - 1511014980 * q^85 + 1609139286 * q^86 + 2211977448 * q^87 + 5719474092 * q^88 + 879649008 * q^89 + 527976792 * q^90 - 1373054348 * q^91 - 1614694368 * q^92 - 3089271597 * q^93 - 5912472648 * q^94 + 1203940032 * q^95 + 260186436 * q^96 + 1793848732 * q^97 + 7812444678 * q^98 + 8253694242 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.10.a	\(\chi_{21}(1, \cdot)\)	21.10.a.a	1	1
		21.10.a.b	2
		21.10.a.c	2
		21.10.a.d	3
21.10.c	\(\chi_{21}(20, \cdot)\)	21.10.c.a	2	1
		21.10.c.b	20
21.10.e	\(\chi_{21}(4, \cdot)\)	21.10.e.a	10	2
		21.10.e.b	14
21.10.g	\(\chi_{21}(5, \cdot)\)	21.10.g.a	44	2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)