Space of modular forms of level 672 and weight 2

• Label: 672.2
• Level: 672
• Weight: 2
• Dimension: 4868
• Nonzero newspaces: 24
• Newform subspaces: 69
• Sturm bound: 49152
• Trace bound: 14

Defining parameters

Level:	\( N \)	=	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 69 \)
Sturm bound:			\(49152\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(672))\).

	Total	New	Old
Modular forms	13056	5068	7988
Cusp forms	11521	4868	6653
Eisenstein series	1535	200	1335

Trace form

4868 * q - 14 * q^3 - 32 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 32 * q^9 + 16 * q^12 - 8 * q^13 + 32 * q^14 - 12 * q^15 + 48 * q^16 + 32 * q^17 - 12 * q^19 + 64 * q^20 - 4 * q^21 - 32 * q^22 + 48 * q^23 - 40 * q^24 - 12 * q^25 - 80 * q^26 + 64 * q^27 - 80 * q^28 - 8 * q^29 - 112 * q^30 + 68 * q^31 - 80 * q^32 - 44 * q^33 - 80 * q^34 + 48 * q^35 - 144 * q^36 - 72 * q^37 - 80 * q^38 + 40 * q^39 - 112 * q^40 - 16 * q^41 - 80 * q^42 - 40 * q^43 - 16 * q^44 - 40 * q^45 - 32 * q^46 + 24 * q^47 - 120 * q^48 + 20 * q^49 - 48 * q^50 + 10 * q^51 - 128 * q^52 + 120 * q^53 - 120 * q^54 - 64 * q^55 - 56 * q^56 - 8 * q^57 - 176 * q^58 - 32 * q^59 - 136 * q^60 + 184 * q^61 - 96 * q^62 + 30 * q^63 - 224 * q^64 + 80 * q^65 - 64 * q^66 - 52 * q^67 + 16 * q^68 + 160 * q^69 - 64 * q^70 - 56 * q^71 + 104 * q^72 + 32 * q^73 + 64 * q^74 - 64 * q^75 - 32 * q^76 + 64 * q^77 + 88 * q^78 - 28 * q^79 + 112 * q^80 + 64 * q^81 + 128 * q^82 + 112 * q^84 + 48 * q^85 + 128 * q^86 - 128 * q^87 + 144 * q^88 + 248 * q^90 - 112 * q^91 + 112 * q^92 - 88 * q^93 - 144 * q^94 - 104 * q^95 + 24 * q^96 - 256 * q^97 - 256 * q^98 - 212 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(672))\)

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
672.2.a	\(\chi_{672}(1, \cdot)\)	672.2.a.a	1	1
		672.2.a.b	1
		672.2.a.c	1
		672.2.a.d	1
		672.2.a.e	1
		672.2.a.f	1
		672.2.a.g	1
		672.2.a.h	1
		672.2.a.i	2
		672.2.a.j	2
672.2.b	\(\chi_{672}(223, \cdot)\)	672.2.b.a	8	1
		672.2.b.b	8
672.2.c	\(\chi_{672}(337, \cdot)\)	672.2.c.a	4	1
		672.2.c.b	8
672.2.h	\(\chi_{672}(575, \cdot)\)	672.2.h.a	4	1
		672.2.h.b	4
		672.2.h.c	4
		672.2.h.d	4
		672.2.h.e	8
672.2.i	\(\chi_{672}(209, \cdot)\)	672.2.i.a	4	1
		672.2.i.b	4
		672.2.i.c	4
		672.2.i.d	8
		672.2.i.e	8
672.2.j	\(\chi_{672}(239, \cdot)\)	672.2.j.a	4	1
		672.2.j.b	4
		672.2.j.c	4
		672.2.j.d	12
672.2.k	\(\chi_{672}(545, \cdot)\)	672.2.k.a	8	1
		672.2.k.b	8
		672.2.k.c	8
		672.2.k.d	8
672.2.p	\(\chi_{672}(559, \cdot)\)	672.2.p.a	16	1
672.2.q	\(\chi_{672}(193, \cdot)\)	672.2.q.a	2	2
		672.2.q.b	2
		672.2.q.c	2
		672.2.q.d	2
		672.2.q.e	2
		672.2.q.f	2
		672.2.q.g	2
		672.2.q.h	2
		672.2.q.i	2
		672.2.q.j	2
		672.2.q.k	6
		672.2.q.l	6
672.2.s	\(\chi_{672}(71, \cdot)\)	None	0	2
672.2.u	\(\chi_{672}(55, \cdot)\)	None	0	2
672.2.w	\(\chi_{672}(169, \cdot)\)	None	0	2
672.2.y	\(\chi_{672}(41, \cdot)\)	None	0	2
672.2.bb	\(\chi_{672}(271, \cdot)\)	672.2.bb.a	32	2
672.2.bc	\(\chi_{672}(257, \cdot)\)	672.2.bc.a	4	2
		672.2.bc.b	4
		672.2.bc.c	8
		672.2.bc.d	16
		672.2.bc.e	32
672.2.bd	\(\chi_{672}(431, \cdot)\)	672.2.bd.a	56	2
672.2.bi	\(\chi_{672}(17, \cdot)\)	672.2.bi.a	4	2
		672.2.bi.b	4
		672.2.bi.c	48
672.2.bj	\(\chi_{672}(95, \cdot)\)	672.2.bj.a	64	2
672.2.bk	\(\chi_{672}(529, \cdot)\)	672.2.bk.a	32	2
672.2.bl	\(\chi_{672}(31, \cdot)\)	672.2.bl.a	16	2
		672.2.bl.b	16
672.2.bo	\(\chi_{672}(125, \cdot)\)	672.2.bo.a	496	4
672.2.bq	\(\chi_{672}(85, \cdot)\)	672.2.bq.a	88	4
		672.2.bq.b	104
672.2.bs	\(\chi_{672}(155, \cdot)\)	672.2.bs.a	192	4
		672.2.bs.b	192
672.2.bu	\(\chi_{672}(139, \cdot)\)	672.2.bu.a	256	4
672.2.bw	\(\chi_{672}(89, \cdot)\)	None	0	4
672.2.by	\(\chi_{672}(25, \cdot)\)	None	0	4
672.2.ca	\(\chi_{672}(103, \cdot)\)	None	0	4
672.2.cc	\(\chi_{672}(23, \cdot)\)	None	0	4
672.2.cf	\(\chi_{672}(19, \cdot)\)	672.2.cf.a	512	8
672.2.ch	\(\chi_{672}(11, \cdot)\)	672.2.ch.a	992	8
672.2.cj	\(\chi_{672}(37, \cdot)\)	672.2.cj.a	512	8
672.2.cl	\(\chi_{672}(5, \cdot)\)	672.2.cl.a	992	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(672))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(672)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)