Space of modular forms of level 1156 and weight 4

• Label: 1156.4
• Level: 1156
• Weight: 4
• Dimension: 71956
• Nonzero newspaces: 10
• Sturm bound: 332928
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(332928\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1156))\).

	Total	New	Old
Modular forms	125848	72692	53156
Cusp forms	123848	71956	51892
Eisenstein series	2000	736	1264

Trace form

71956 * q - 120 * q^2 - 120 * q^4 - 240 * q^5 - 120 * q^6 - 120 * q^8 - 240 * q^9 - 120 * q^10 + 224 * q^11 - 120 * q^12 - 304 * q^13 - 120 * q^14 - 672 * q^15 - 136 * q^16 - 384 * q^17 - 232 * q^18 - 160 * q^19 - 120 * q^20 - 48 * q^21 - 120 * q^22 + 416 * q^23 - 1944 * q^24 - 904 * q^25 - 1592 * q^26 - 432 * q^27 + 168 * q^28 + 280 * q^29 + 2568 * q^30 + 1728 * q^31 + 2360 * q^32 + 1840 * q^33 + 1984 * q^34 + 1984 * q^35 + 3336 * q^36 + 1104 * q^37 + 920 * q^38 + 2816 * q^39 - 1272 * q^40 + 760 * q^41 - 3864 * q^42 - 2544 * q^43 - 5048 * q^44 - 5480 * q^45 - 4056 * q^46 - 3040 * q^47 + 312 * q^48 - 3312 * q^49 - 136 * q^50 - 1600 * q^51 - 232 * q^52 - 6488 * q^53 + 8648 * q^54 - 4768 * q^55 + 5080 * q^56 - 8448 * q^57 + 2456 * q^58 + 1248 * q^59 - 2408 * q^60 + 4080 * q^61 - 4264 * q^62 + 9600 * q^63 - 5400 * q^64 + 18056 * q^65 - 13768 * q^66 + 2144 * q^67 - 6024 * q^68 + 17008 * q^69 - 10984 * q^70 + 4896 * q^71 - 9896 * q^72 + 11592 * q^73 - 2520 * q^74 + 1440 * q^75 + 440 * q^76 - 4240 * q^77 + 8824 * q^78 - 5536 * q^79 + 7848 * q^80 - 27392 * q^81 + 11320 * q^82 - 13328 * q^83 - 136 * q^84 - 12628 * q^85 - 22472 * q^86 - 17952 * q^87 - 10488 * q^88 - 8592 * q^89 - 5560 * q^90 - 5184 * q^91 + 2344 * q^92 + 2704 * q^93 + 8520 * q^94 + 11104 * q^95 + 21464 * q^96 + 9552 * q^97 + 24088 * q^98 + 32144 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1156))\)

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
1156.4.a	\(\chi_{1156}(1, \cdot)\)	1156.4.a.a	1	1
		1156.4.a.b	2
		1156.4.a.c	2
		1156.4.a.d	2
		1156.4.a.e	2
		1156.4.a.f	2
		1156.4.a.g	3
		1156.4.a.h	4
		1156.4.a.i	6
		1156.4.a.j	12
		1156.4.a.k	12
		1156.4.a.l	20
1156.4.b	\(\chi_{1156}(577, \cdot)\)	1156.4.b.a	2	1
		1156.4.b.b	2
		1156.4.b.c	4
		1156.4.b.d	4
		1156.4.b.e	6
		1156.4.b.f	6
		1156.4.b.g	20
		1156.4.b.h	24
1156.4.e	\(\chi_{1156}(829, \cdot)\)	n/a	136	2
1156.4.h	\(\chi_{1156}(733, \cdot)\)	n/a	268	4
1156.4.i	\(\chi_{1156}(75, \cdot)\)	n/a	3128	8
1156.4.k	\(\chi_{1156}(69, \cdot)\)	n/a	1216	16
1156.4.n	\(\chi_{1156}(33, \cdot)\)	n/a	1216	16
1156.4.p	\(\chi_{1156}(13, \cdot)\)	n/a	2432	32
1156.4.q	\(\chi_{1156}(9, \cdot)\)	n/a	4928	64
1156.4.t	\(\chi_{1156}(3, \cdot)\)	n/a	58496	128

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1156))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1156)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 1}\)