Space of modular forms of level 196 and weight 10

• Label: 196.10
• Level: 196
• Weight: 10
• Dimension: 5875
• Nonzero newspaces: 8
• Sturm bound: 23520
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(23520\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(196))\).

	Total	New	Old
Modular forms	10734	5971	4763
Cusp forms	10434	5875	4559
Eisenstein series	300	96	204

Trace form

5875 * q - 15 * q^2 - 96 * q^3 - 15 * q^4 - 2400 * q^5 - 21 * q^6 - 1368 * q^7 + 49647 * q^8 - 69117 * q^9 + 53427 * q^10 + 162948 * q^11 - 166005 * q^12 + 14120 * q^13 - 165846 * q^14 + 1527288 * q^15 + 1611609 * q^16 - 811464 * q^17 - 3072447 * q^18 - 196456 * q^19 - 21 * q^20 - 218580 * q^21 + 141645 * q^22 - 1296912 * q^23 - 11942493 * q^24 - 2348339 * q^25 + 8732163 * q^26 + 18524304 * q^27 + 9760806 * q^28 - 8631528 * q^29 - 44027229 * q^30 + 31638992 * q^31 + 1794225 * q^32 - 24798858 * q^33 - 21 * q^34 - 3762690 * q^35 + 99606063 * q^36 + 168596060 * q^37 + 4053363 * q^38 - 168008994 * q^39 - 104904525 * q^40 - 145997856 * q^41 - 48867369 * q^42 + 80779496 * q^43 - 12606609 * q^44 + 235040388 * q^45 + 453704775 * q^46 - 28697748 * q^47 - 433741530 * q^49 - 763698558 * q^50 - 1773864 * q^51 - 145586613 * q^52 + 759939708 * q^53 + 1039847667 * q^54 + 78977646 * q^55 + 287469978 * q^56 - 156198294 * q^57 - 540523545 * q^58 - 839583132 * q^59 - 1860382341 * q^60 + 999385484 * q^61 - 21 * q^62 + 327985500 * q^63 + 1747109319 * q^64 + 986358402 * q^65 + 1618568235 * q^66 - 988185436 * q^67 - 2547260301 * q^68 - 993618978 * q^69 - 1613175549 * q^70 - 1105279560 * q^71 + 3200099481 * q^72 - 83103232 * q^73 + 2535833775 * q^74 + 2502461952 * q^75 - 21 * q^76 + 1496152098 * q^77 - 2995584279 * q^78 + 657822104 * q^79 - 692420310 * q^80 - 11945443149 * q^81 - 4336028646 * q^82 - 3503571156 * q^83 + 13443746274 * q^84 + 771316746 * q^85 + 8403404184 * q^86 + 3430003992 * q^87 - 6537634026 * q^88 + 7184460132 * q^89 - 27224795052 * q^90 - 2734354314 * q^91 - 2214773700 * q^92 - 7578082710 * q^93 + 585265458 * q^94 + 1224352152 * q^95 + 28751453856 * q^96 - 2388951850 * q^97 + 23986827180 * q^98 + 1994871564 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(196))\)

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
196.10.a	\(\chi_{196}(1, \cdot)\)	196.10.a.a	1	1
		196.10.a.b	2
		196.10.a.c	2
		196.10.a.d	4
		196.10.a.e	6
		196.10.a.f	6
		196.10.a.g	10
196.10.d	\(\chi_{196}(195, \cdot)\)	n/a	176	1
196.10.e	\(\chi_{196}(165, \cdot)\)	196.10.e.a	2	2
		196.10.e.b	2
		196.10.e.c	4
		196.10.e.d	4
		196.10.e.e	4
		196.10.e.f	4
		196.10.e.g	8
		196.10.e.h	12
		196.10.e.i	20
196.10.f	\(\chi_{196}(19, \cdot)\)	n/a	352	2
196.10.i	\(\chi_{196}(29, \cdot)\)	n/a	252	6
196.10.j	\(\chi_{196}(27, \cdot)\)	n/a	1500	6
196.10.m	\(\chi_{196}(9, \cdot)\)	n/a	504	12
196.10.p	\(\chi_{196}(3, \cdot)\)	n/a	3000	12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(196))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(196)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)