Space of modular forms of level 616 and weight 2

• Label: 616.2
• Level: 616
• Weight: 2
• Dimension: 5926
• Nonzero newspaces: 24
• Newform subspaces: 61
• Sturm bound: 46080
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 61 \)
Sturm bound:			\(46080\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(616))\).

	Total	New	Old
Modular forms	12240	6286	5954
Cusp forms	10801	5926	4875
Eisenstein series	1439	360	1079

Trace form

5926 * q - 28 * q^2 - 28 * q^3 - 28 * q^4 - 28 * q^6 - 38 * q^7 - 76 * q^8 - 44 * q^9 - 28 * q^10 - 28 * q^11 - 68 * q^12 + 12 * q^13 - 38 * q^14 - 32 * q^15 - 28 * q^16 - 24 * q^17 - 64 * q^18 + 2 * q^19 - 64 * q^20 + 20 * q^21 - 118 * q^22 - 84 * q^23 - 100 * q^24 - 52 * q^25 - 88 * q^26 - 58 * q^27 - 134 * q^28 + 20 * q^29 - 184 * q^30 - 44 * q^31 - 108 * q^32 - 104 * q^33 - 220 * q^34 - 68 * q^35 - 296 * q^36 + 12 * q^37 - 164 * q^38 - 160 * q^39 - 228 * q^40 - 68 * q^41 - 76 * q^42 - 156 * q^43 - 150 * q^44 - 48 * q^45 - 108 * q^46 - 124 * q^47 - 128 * q^48 - 118 * q^49 - 132 * q^50 - 222 * q^51 - 20 * q^52 + 28 * q^53 - 44 * q^54 - 84 * q^55 - 44 * q^56 - 150 * q^57 + 12 * q^58 - 30 * q^59 + 4 * q^60 + 40 * q^61 + 80 * q^62 - 100 * q^63 + 8 * q^64 + 24 * q^65 - 10 * q^66 - 24 * q^67 - 28 * q^68 + 56 * q^69 - 16 * q^70 - 108 * q^71 + 36 * q^72 - 40 * q^73 - 96 * q^74 - 238 * q^75 - 12 * q^76 - 8 * q^77 - 104 * q^78 - 224 * q^79 - 36 * q^80 - 154 * q^81 + 28 * q^82 - 290 * q^83 - 134 * q^84 - 120 * q^85 - 124 * q^86 - 332 * q^87 + 214 * q^88 - 208 * q^89 + 96 * q^90 - 124 * q^91 - 72 * q^92 - 72 * q^93 + 140 * q^94 - 176 * q^95 + 64 * q^96 - 182 * q^97 + 24 * q^98 - 116 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)

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
616.2.a	\(\chi_{616}(1, \cdot)\)	616.2.a.a	1	1
		616.2.a.b	1
		616.2.a.c	1
		616.2.a.d	1
		616.2.a.e	1
		616.2.a.f	2
		616.2.a.g	3
		616.2.a.h	4
616.2.c	\(\chi_{616}(309, \cdot)\)	616.2.c.a	2	1
		616.2.c.b	4
		616.2.c.c	24
		616.2.c.d	30
616.2.e	\(\chi_{616}(153, \cdot)\)	616.2.e.a	24	1
616.2.f	\(\chi_{616}(351, \cdot)\)	None	0	1
616.2.h	\(\chi_{616}(419, \cdot)\)	616.2.h.a	40	1
		616.2.h.b	40
616.2.j	\(\chi_{616}(111, \cdot)\)	None	0	1
616.2.l	\(\chi_{616}(43, \cdot)\)	616.2.l.a	2	1
		616.2.l.b	2
		616.2.l.c	34
		616.2.l.d	34
616.2.o	\(\chi_{616}(461, \cdot)\)	616.2.o.a	2	1
		616.2.o.b	2
		616.2.o.c	88
616.2.q	\(\chi_{616}(177, \cdot)\)	616.2.q.a	2	2
		616.2.q.b	4
		616.2.q.c	6
		616.2.q.d	8
		616.2.q.e	10
		616.2.q.f	10
616.2.r	\(\chi_{616}(113, \cdot)\)	616.2.r.a	4	4
		616.2.r.b	4
		616.2.r.c	12
		616.2.r.d	16
		616.2.r.e	16
		616.2.r.f	20
616.2.s	\(\chi_{616}(285, \cdot)\)	616.2.s.a	184	2
616.2.w	\(\chi_{616}(199, \cdot)\)	None	0	2
616.2.y	\(\chi_{616}(219, \cdot)\)	616.2.y.a	8	2
		616.2.y.b	176
616.2.ba	\(\chi_{616}(263, \cdot)\)	None	0	2
616.2.bc	\(\chi_{616}(243, \cdot)\)	616.2.bc.a	80	2
		616.2.bc.b	80
616.2.bd	\(\chi_{616}(221, \cdot)\)	616.2.bd.a	4	2
		616.2.bd.b	4
		616.2.bd.c	152
616.2.bf	\(\chi_{616}(241, \cdot)\)	616.2.bf.a	48	2
616.2.bi	\(\chi_{616}(13, \cdot)\)	616.2.bi.a	8	4
		616.2.bi.b	8
		616.2.bi.c	352
616.2.bl	\(\chi_{616}(211, \cdot)\)	616.2.bl.a	144	4
		616.2.bl.b	144
616.2.bn	\(\chi_{616}(223, \cdot)\)	None	0	4
616.2.bp	\(\chi_{616}(27, \cdot)\)	616.2.bp.a	8	4
		616.2.bp.b	8
		616.2.bp.c	352
616.2.br	\(\chi_{616}(127, \cdot)\)	None	0	4
616.2.bs	\(\chi_{616}(41, \cdot)\)	616.2.bs.a	96	4
616.2.bu	\(\chi_{616}(141, \cdot)\)	616.2.bu.a	136	4
		616.2.bu.b	152
616.2.bw	\(\chi_{616}(9, \cdot)\)	616.2.bw.a	96	8
		616.2.bw.b	96
616.2.by	\(\chi_{616}(17, \cdot)\)	616.2.by.a	192	8
616.2.ca	\(\chi_{616}(37, \cdot)\)	616.2.ca.a	736	8
616.2.cb	\(\chi_{616}(3, \cdot)\)	616.2.cb.a	736	8
616.2.cd	\(\chi_{616}(39, \cdot)\)	None	0	8
616.2.cf	\(\chi_{616}(51, \cdot)\)	616.2.cf.a	736	8
616.2.ch	\(\chi_{616}(31, \cdot)\)	None	0	8
616.2.cl	\(\chi_{616}(61, \cdot)\)	616.2.cl.a	736	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(616))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(616)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 2}\)