Space of modular forms of level 1617 and weight 4

• Label: 1617.4
• Level: 1617
• Weight: 4
• Dimension: 198872
• Nonzero newspaces: 32
• Sturm bound: 752640
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(752640\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1617))\).

	Total	New	Old
Modular forms	284640	200620	84020
Cusp forms	279840	198872	80968
Eisenstein series	4800	1748	3052

Trace form

198872 * q - 101 * q^3 - 250 * q^4 - 96 * q^5 - 207 * q^6 - 384 * q^7 + 136 * q^8 - 37 * q^9 - 224 * q^10 - 100 * q^11 - 812 * q^12 - 602 * q^13 - 624 * q^14 - 679 * q^15 + 30 * q^16 + 252 * q^17 + 1107 * q^18 + 1556 * q^19 + 3226 * q^20 + 1032 * q^21 - 868 * q^22 - 1052 * q^23 - 547 * q^24 - 2290 * q^25 - 1226 * q^26 - 515 * q^27 - 2496 * q^28 - 1892 * q^29 - 4298 * q^30 - 1846 * q^31 - 3092 * q^32 + 69 * q^33 + 240 * q^34 + 168 * q^35 + 2055 * q^36 - 3986 * q^37 - 4226 * q^38 - 451 * q^39 - 8188 * q^40 - 2796 * q^41 + 5514 * q^42 + 7088 * q^43 + 10654 * q^44 + 8690 * q^45 + 21984 * q^46 + 9716 * q^47 + 8340 * q^48 + 11160 * q^49 + 994 * q^50 - 6378 * q^51 + 840 * q^52 - 3376 * q^53 - 17280 * q^54 + 352 * q^55 - 2652 * q^56 - 1968 * q^57 - 1916 * q^58 - 12780 * q^59 - 18806 * q^60 - 27362 * q^61 - 44664 * q^62 - 7380 * q^63 - 34114 * q^64 - 14784 * q^65 - 7545 * q^66 + 3116 * q^67 + 1616 * q^68 + 2578 * q^69 + 4956 * q^70 + 21972 * q^71 + 23902 * q^72 + 10970 * q^73 + 24630 * q^74 + 25116 * q^75 + 64688 * q^76 + 13500 * q^77 + 21958 * q^78 + 19334 * q^79 + 26706 * q^80 + 5495 * q^81 - 21014 * q^82 - 16648 * q^83 - 16296 * q^84 - 12026 * q^85 - 15956 * q^86 - 13272 * q^87 - 52258 * q^88 - 21308 * q^89 - 14990 * q^90 - 4308 * q^91 - 47090 * q^92 + 6993 * q^93 + 23900 * q^94 + 38208 * q^95 + 40678 * q^96 + 39452 * q^97 + 102108 * q^98 + 11513 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1617))\)

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
1617.4.a	\(\chi_{1617}(1, \cdot)\)	1617.4.a.a	1	1
		1617.4.a.b	1
		1617.4.a.c	1
		1617.4.a.d	1
		1617.4.a.e	1
		1617.4.a.f	1
		1617.4.a.g	1
		1617.4.a.h	2
		1617.4.a.i	2
		1617.4.a.j	2
		1617.4.a.k	2
		1617.4.a.l	2
		1617.4.a.m	2
		1617.4.a.n	5
		1617.4.a.o	5
		1617.4.a.p	5
		1617.4.a.q	7
		1617.4.a.r	7
		1617.4.a.s	7
		1617.4.a.t	7
		1617.4.a.u	8
		1617.4.a.v	8
		1617.4.a.w	10
		1617.4.a.x	10
		1617.4.a.y	10
		1617.4.a.z	10
		1617.4.a.ba	12
		1617.4.a.bb	12
		1617.4.a.bc	16
		1617.4.a.bd	16
		1617.4.a.be	16
		1617.4.a.bf	16
1617.4.c	\(\chi_{1617}(538, \cdot)\)	n/a	240	1
1617.4.e	\(\chi_{1617}(881, \cdot)\)	n/a	400	1
1617.4.g	\(\chi_{1617}(197, \cdot)\)	n/a	482	1
1617.4.i	\(\chi_{1617}(67, \cdot)\)	n/a	400	2
1617.4.j	\(\chi_{1617}(148, \cdot)\)	n/a	984	4
1617.4.l	\(\chi_{1617}(263, \cdot)\)	n/a	944	2
1617.4.n	\(\chi_{1617}(815, \cdot)\)	n/a	800	2
1617.4.p	\(\chi_{1617}(472, \cdot)\)	n/a	480	2
1617.4.r	\(\chi_{1617}(232, \cdot)\)	n/a	1680	6
1617.4.t	\(\chi_{1617}(50, \cdot)\)	n/a	1928	4
1617.4.v	\(\chi_{1617}(146, \cdot)\)	n/a	1888	4
1617.4.x	\(\chi_{1617}(244, \cdot)\)	n/a	960	4
1617.4.ba	\(\chi_{1617}(428, \cdot)\)	n/a	4008	6
1617.4.bc	\(\chi_{1617}(188, \cdot)\)	n/a	3360	6
1617.4.be	\(\chi_{1617}(76, \cdot)\)	n/a	2016	6
1617.4.bg	\(\chi_{1617}(214, \cdot)\)	n/a	1920	8
1617.4.bh	\(\chi_{1617}(100, \cdot)\)	n/a	3360	12
1617.4.bj	\(\chi_{1617}(19, \cdot)\)	n/a	1920	8
1617.4.bl	\(\chi_{1617}(80, \cdot)\)	n/a	3776	8
1617.4.bn	\(\chi_{1617}(116, \cdot)\)	n/a	3776	8
1617.4.bp	\(\chi_{1617}(64, \cdot)\)	n/a	8064	24
1617.4.br	\(\chi_{1617}(10, \cdot)\)	n/a	4032	12
1617.4.bt	\(\chi_{1617}(89, \cdot)\)	n/a	6720	12
1617.4.bv	\(\chi_{1617}(32, \cdot)\)	n/a	8016	12
1617.4.by	\(\chi_{1617}(13, \cdot)\)	n/a	8064	24
1617.4.ca	\(\chi_{1617}(20, \cdot)\)	n/a	16032	24
1617.4.cc	\(\chi_{1617}(8, \cdot)\)	n/a	16032	24
1617.4.ce	\(\chi_{1617}(4, \cdot)\)	n/a	16128	48
1617.4.cg	\(\chi_{1617}(2, \cdot)\)	n/a	32064	48
1617.4.ci	\(\chi_{1617}(5, \cdot)\)	n/a	32064	48
1617.4.ck	\(\chi_{1617}(40, \cdot)\)	n/a	16128	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1617))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1617)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 2}\)