Space of modular forms of level 336 and weight 2

• Label: 336.2
• Level: 336
• Weight: 2
• Dimension: 1196
• Nonzero newspaces: 16
• Newform subspaces: 56
• Sturm bound: 12288
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 56 \)
Sturm bound:			\(12288\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(336))\).

	Total	New	Old
Modular forms	3408	1288	2120
Cusp forms	2737	1196	1541
Eisenstein series	671	92	579

Trace form

1196 * q - 7 * q^3 - 8 * q^4 + 4 * q^5 + 4 * q^6 - 10 * q^7 + 24 * q^8 + 7 * q^9 - 8 * q^10 + 24 * q^11 - 12 * q^12 - 4 * q^13 - 12 * q^14 + 2 * q^15 - 56 * q^16 - 4 * q^17 - 28 * q^18 + 26 * q^19 - 32 * q^20 - 7 * q^21 - 80 * q^22 + 20 * q^23 - 68 * q^24 + 24 * q^25 - 40 * q^26 - 28 * q^27 - 24 * q^28 + 44 * q^29 - 52 * q^30 - 2 * q^31 + 13 * q^33 - 8 * q^34 + 12 * q^35 - 56 * q^36 + 62 * q^37 + 16 * q^38 - 48 * q^39 + 24 * q^40 + 12 * q^41 - 40 * q^42 - 48 * q^43 - 16 * q^44 - 35 * q^45 - 48 * q^46 - 36 * q^47 - 4 * q^48 - 84 * q^49 - 96 * q^50 - 107 * q^51 - 176 * q^52 - 124 * q^53 - 84 * q^54 - 160 * q^55 - 168 * q^56 - 86 * q^57 - 224 * q^58 - 104 * q^59 - 196 * q^60 - 234 * q^61 - 192 * q^62 - 47 * q^63 - 344 * q^64 - 72 * q^65 - 236 * q^66 - 86 * q^67 - 184 * q^68 - 140 * q^69 - 192 * q^70 + 4 * q^71 - 180 * q^72 - 66 * q^73 - 104 * q^74 - 40 * q^75 - 152 * q^76 - 16 * q^77 - 120 * q^78 + 14 * q^79 - 16 * q^80 - 89 * q^81 - 72 * q^82 + 72 * q^83 - 4 * q^84 - 84 * q^85 + 32 * q^86 + 36 * q^87 + 40 * q^88 + 12 * q^89 + 36 * q^90 - 164 * q^91 + 56 * q^92 - 43 * q^93 + 200 * q^94 - 68 * q^95 + 220 * q^96 + 20 * q^97 + 208 * q^98 + 14 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)

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
336.2.a	\(\chi_{336}(1, \cdot)\)	336.2.a.a	1	1
		336.2.a.b	1
		336.2.a.c	1
		336.2.a.d	1
		336.2.a.e	1
		336.2.a.f	1
336.2.b	\(\chi_{336}(223, \cdot)\)	336.2.b.a	2	1
		336.2.b.b	2
		336.2.b.c	2
		336.2.b.d	2
336.2.c	\(\chi_{336}(169, \cdot)\)	None	0	1
336.2.h	\(\chi_{336}(239, \cdot)\)	336.2.h.a	4	1
		336.2.h.b	8
336.2.i	\(\chi_{336}(41, \cdot)\)	None	0	1
336.2.j	\(\chi_{336}(71, \cdot)\)	None	0	1
336.2.k	\(\chi_{336}(209, \cdot)\)	336.2.k.a	2	1
		336.2.k.b	4
		336.2.k.c	8
336.2.p	\(\chi_{336}(55, \cdot)\)	None	0	1
336.2.q	\(\chi_{336}(193, \cdot)\)	336.2.q.a	2	2
		336.2.q.b	2
		336.2.q.c	2
		336.2.q.d	2
		336.2.q.e	2
		336.2.q.f	2
		336.2.q.g	4
336.2.s	\(\chi_{336}(155, \cdot)\)	336.2.s.a	4	2
		336.2.s.b	4
		336.2.s.c	40
		336.2.s.d	48
336.2.u	\(\chi_{336}(139, \cdot)\)	336.2.u.a	64	2
336.2.w	\(\chi_{336}(85, \cdot)\)	336.2.w.a	20	2
		336.2.w.b	28
336.2.y	\(\chi_{336}(125, \cdot)\)	336.2.y.a	120	2
336.2.bb	\(\chi_{336}(103, \cdot)\)	None	0	2
336.2.bc	\(\chi_{336}(17, \cdot)\)	336.2.bc.a	2	2
		336.2.bc.b	2
		336.2.bc.c	2
		336.2.bc.d	2
		336.2.bc.e	4
		336.2.bc.f	16
336.2.bd	\(\chi_{336}(23, \cdot)\)	None	0	2
336.2.bi	\(\chi_{336}(89, \cdot)\)	None	0	2
336.2.bj	\(\chi_{336}(95, \cdot)\)	336.2.bj.a	2	2
		336.2.bj.b	2
		336.2.bj.c	2
		336.2.bj.d	2
		336.2.bj.e	8
		336.2.bj.f	8
		336.2.bj.g	8
336.2.bk	\(\chi_{336}(25, \cdot)\)	None	0	2
336.2.bl	\(\chi_{336}(31, \cdot)\)	336.2.bl.a	2	2
		336.2.bl.b	2
		336.2.bl.c	2
		336.2.bl.d	2
		336.2.bl.e	2
		336.2.bl.f	2
		336.2.bl.g	2
		336.2.bl.h	2
336.2.bo	\(\chi_{336}(5, \cdot)\)	336.2.bo.a	240	4
336.2.bq	\(\chi_{336}(37, \cdot)\)	336.2.bq.a	8	4
		336.2.bq.b	120
336.2.bs	\(\chi_{336}(19, \cdot)\)	336.2.bs.a	128	4
336.2.bu	\(\chi_{336}(11, \cdot)\)	336.2.bu.a	240	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(336))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(336)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)