Space of modular forms of level 1617 and weight 2

• Label: 1617.2
• Level: 1617
• Weight: 2
• Dimension: 65706
• Nonzero newspaces: 32
• Sturm bound: 376320
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(376320\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1617))\).

	Total	New	Old
Modular forms	96480	67454	29026
Cusp forms	91681	65706	25975
Eisenstein series	4799	1748	3051

Trace form

65706 * q - 6 * q^2 - 123 * q^3 - 232 * q^4 + 12 * q^5 - 90 * q^6 - 272 * q^7 + 62 * q^8 - 89 * q^9 - 136 * q^10 + 34 * q^11 - 222 * q^12 - 188 * q^13 + 48 * q^14 - 189 * q^15 - 108 * q^16 + 42 * q^17 - 104 * q^18 - 180 * q^19 + 110 * q^20 - 130 * q^21 - 400 * q^22 + 68 * q^23 - 46 * q^24 - 104 * q^25 + 134 * q^26 - 114 * q^27 - 144 * q^28 + 104 * q^29 - 48 * q^30 - 118 * q^31 + 158 * q^32 - 120 * q^33 - 364 * q^34 + 84 * q^35 - 214 * q^36 - 214 * q^37 - 22 * q^38 - 158 * q^39 - 464 * q^40 - 96 * q^41 - 282 * q^42 - 420 * q^43 - 58 * q^44 - 295 * q^45 - 456 * q^46 + 22 * q^47 - 362 * q^48 - 516 * q^49 - 52 * q^50 - 214 * q^51 - 540 * q^52 - 14 * q^53 - 104 * q^54 - 326 * q^55 - 300 * q^56 - 150 * q^57 - 316 * q^58 + 78 * q^59 - 592 * q^60 - 368 * q^61 - 12 * q^62 - 198 * q^63 - 780 * q^64 - 108 * q^65 - 583 * q^66 - 598 * q^67 - 344 * q^68 - 355 * q^69 - 420 * q^70 - 324 * q^71 - 796 * q^72 - 468 * q^73 - 210 * q^74 - 546 * q^75 - 1076 * q^76 - 108 * q^77 - 1010 * q^78 - 304 * q^79 - 894 * q^80 - 785 * q^81 - 692 * q^82 - 398 * q^83 - 868 * q^84 - 816 * q^85 - 928 * q^86 - 648 * q^87 - 1086 * q^88 - 436 * q^89 - 1314 * q^90 - 584 * q^91 - 562 * q^92 - 749 * q^93 - 736 * q^94 - 426 * q^95 - 1020 * q^96 - 306 * q^97 - 876 * q^98 - 551 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1617))\)

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
1617.2.a	\(\chi_{1617}(1, \cdot)\)	1617.2.a.a	1	1
		1617.2.a.b	1
		1617.2.a.c	1
		1617.2.a.d	1
		1617.2.a.e	1
		1617.2.a.f	1
		1617.2.a.g	1
		1617.2.a.h	1
		1617.2.a.i	1
		1617.2.a.j	1
		1617.2.a.k	2
		1617.2.a.l	2
		1617.2.a.m	2
		1617.2.a.n	2
		1617.2.a.o	2
		1617.2.a.p	2
		1617.2.a.q	3
		1617.2.a.r	3
		1617.2.a.s	3
		1617.2.a.t	3
		1617.2.a.u	4
		1617.2.a.v	4
		1617.2.a.w	4
		1617.2.a.x	4
		1617.2.a.y	4
		1617.2.a.z	4
		1617.2.a.ba	5
		1617.2.a.bb	5
1617.2.c	\(\chi_{1617}(538, \cdot)\)	1617.2.c.a	32	1
		1617.2.c.b	48
1617.2.e	\(\chi_{1617}(881, \cdot)\)	n/a	132	1
1617.2.g	\(\chi_{1617}(197, \cdot)\)	n/a	154	1
1617.2.i	\(\chi_{1617}(67, \cdot)\)	n/a	132	2
1617.2.j	\(\chi_{1617}(148, \cdot)\)	n/a	328	4
1617.2.l	\(\chi_{1617}(263, \cdot)\)	n/a	304	2
1617.2.n	\(\chi_{1617}(815, \cdot)\)	n/a	268	2
1617.2.p	\(\chi_{1617}(472, \cdot)\)	n/a	160	2
1617.2.r	\(\chi_{1617}(232, \cdot)\)	n/a	552	6
1617.2.t	\(\chi_{1617}(50, \cdot)\)	n/a	616	4
1617.2.v	\(\chi_{1617}(146, \cdot)\)	n/a	608	4
1617.2.x	\(\chi_{1617}(244, \cdot)\)	n/a	320	4
1617.2.ba	\(\chi_{1617}(428, \cdot)\)	n/a	1320	6
1617.2.bc	\(\chi_{1617}(188, \cdot)\)	n/a	1128	6
1617.2.be	\(\chi_{1617}(76, \cdot)\)	n/a	672	6
1617.2.bg	\(\chi_{1617}(214, \cdot)\)	n/a	640	8
1617.2.bh	\(\chi_{1617}(100, \cdot)\)	n/a	1128	12
1617.2.bj	\(\chi_{1617}(19, \cdot)\)	n/a	640	8
1617.2.bl	\(\chi_{1617}(80, \cdot)\)	n/a	1216	8
1617.2.bn	\(\chi_{1617}(116, \cdot)\)	n/a	1216	8
1617.2.bp	\(\chi_{1617}(64, \cdot)\)	n/a	2688	24
1617.2.br	\(\chi_{1617}(10, \cdot)\)	n/a	1344	12
1617.2.bt	\(\chi_{1617}(89, \cdot)\)	n/a	2232	12
1617.2.bv	\(\chi_{1617}(32, \cdot)\)	n/a	2640	12
1617.2.by	\(\chi_{1617}(13, \cdot)\)	n/a	2688	24
1617.2.ca	\(\chi_{1617}(20, \cdot)\)	n/a	5280	24
1617.2.cc	\(\chi_{1617}(8, \cdot)\)	n/a	5280	24
1617.2.ce	\(\chi_{1617}(4, \cdot)\)	n/a	5376	48
1617.2.cg	\(\chi_{1617}(2, \cdot)\)	n/a	10560	48
1617.2.ci	\(\chi_{1617}(5, \cdot)\)	n/a	10560	48
1617.2.ck	\(\chi_{1617}(40, \cdot)\)	n/a	5376	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1617))\) into lower level spaces

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