Space of modular forms of level 961 and weight 6

• Label: 961.6
• Level: 961
• Weight: 6
• Dimension: 191140
• Nonzero newspaces: 8
• Sturm bound: 461280
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 961 = 31^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(461280\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(961))\).

	Total	New	Old
Modular forms	192890	192461	429
Cusp forms	191510	191140	370
Eisenstein series	1380	1321	59

Trace form

191140 * q - 435 * q^2 - 435 * q^3 - 435 * q^4 - 435 * q^5 - 435 * q^6 - 435 * q^7 - 435 * q^8 - 435 * q^9 - 435 * q^10 - 435 * q^11 - 435 * q^12 - 435 * q^13 - 435 * q^14 - 435 * q^15 - 435 * q^16 - 435 * q^17 - 435 * q^18 - 435 * q^19 - 435 * q^20 + 18555 * q^21 + 20925 * q^22 - 13965 * q^23 - 86835 * q^24 - 44185 * q^25 - 19395 * q^26 + 6855 * q^27 + 73805 * q^28 + 44865 * q^29 + 107595 * q^30 + 25620 * q^31 + 117225 * q^32 + 16305 * q^33 - 26835 * q^34 - 46935 * q^35 - 207795 * q^36 - 150645 * q^37 - 105795 * q^38 - 98085 * q^39 - 48435 * q^40 + 42735 * q^41 + 260925 * q^42 + 85655 * q^43 - 435 * q^44 - 435 * q^45 - 435 * q^46 - 435 * q^47 + 587175 * q^48 + 117705 * q^49 - 151785 * q^50 - 486255 * q^51 - 506085 * q^52 - 196695 * q^53 - 865365 * q^54 - 194715 * q^55 - 118965 * q^56 + 137985 * q^57 + 394155 * q^58 + 166905 * q^59 + 1539975 * q^60 + 669375 * q^61 + 328860 * q^62 + 774105 * q^63 + 441345 * q^64 + 244545 * q^65 + 13515 * q^66 - 87495 * q^67 - 624345 * q^68 - 790815 * q^69 - 1498665 * q^70 - 751515 * q^71 - 2083065 * q^72 - 328695 * q^73 - 522585 * q^74 + 712575 * q^75 + 2059115 * q^76 + 1151415 * q^77 + 1732155 * q^78 - 368005 * q^79 - 2227635 * q^80 - 984555 * q^81 - 945555 * q^82 - 1411425 * q^83 - 1791795 * q^84 - 344715 * q^85 - 143475 * q^86 + 199845 * q^87 + 1358925 * q^88 + 839415 * q^89 + 2539815 * q^90 + 1040735 * q^91 + 3046635 * q^92 + 1004070 * q^93 + 926025 * q^94 + 1569405 * q^95 + 1757895 * q^96 + 358235 * q^97 + 113325 * q^98 - 353085 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(961))\)

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
961.6.a	\(\chi_{961}(1, \cdot)\)	961.6.a.a	3	1
		961.6.a.b	5
		961.6.a.c	8
		961.6.a.d	10
		961.6.a.e	12
		961.6.a.f	12
		961.6.a.g	26
		961.6.a.h	26
		961.6.a.i	26
		961.6.a.j	48
		961.6.a.k	48
		961.6.a.l	52
		961.6.a.m	96
961.6.c	\(\chi_{961}(439, \cdot)\)	n/a	746	2
961.6.d	\(\chi_{961}(374, \cdot)\)	n/a	1488	4
961.6.g	\(\chi_{961}(235, \cdot)\)	n/a	2984	8
961.6.i	\(\chi_{961}(32, \cdot)\)	n/a	12390	30
961.6.k	\(\chi_{961}(5, \cdot)\)	n/a	24720	60
961.6.l	\(\chi_{961}(2, \cdot)\)	n/a	49560	120
961.6.o	\(\chi_{961}(7, \cdot)\)	n/a	98880	240

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(961))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(961)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)