Space of modular forms of level 1472 and weight 2

• Label: 1472.2
• Level: 1472
• Weight: 2
• Dimension: 37410
• Nonzero newspaces: 16
• Sturm bound: 270336
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(270336\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1472))\).

	Total	New	Old
Modular forms	69168	38334	30834
Cusp forms	66001	37410	28591
Eisenstein series	3167	924	2243

Trace form

37410 * q - 160 * q^2 - 120 * q^3 - 160 * q^4 - 160 * q^5 - 160 * q^6 - 116 * q^7 - 160 * q^8 - 194 * q^9 - 160 * q^10 - 112 * q^11 - 160 * q^12 - 144 * q^13 - 160 * q^14 - 108 * q^15 - 160 * q^16 - 264 * q^17 - 160 * q^18 - 104 * q^19 - 160 * q^20 - 168 * q^21 - 176 * q^22 - 124 * q^23 - 416 * q^24 - 222 * q^25 - 240 * q^26 - 132 * q^27 - 240 * q^28 - 192 * q^29 - 320 * q^30 - 164 * q^31 - 240 * q^32 - 172 * q^33 - 240 * q^34 - 124 * q^35 - 320 * q^36 - 176 * q^37 - 240 * q^38 - 116 * q^39 - 240 * q^40 - 200 * q^41 - 240 * q^42 - 96 * q^43 - 176 * q^44 - 152 * q^45 - 168 * q^46 - 216 * q^47 - 160 * q^48 - 262 * q^49 - 112 * q^50 - 172 * q^51 - 64 * q^52 - 112 * q^53 - 32 * q^54 - 244 * q^55 - 48 * q^56 - 188 * q^57 - 16 * q^58 - 256 * q^59 + 32 * q^60 - 144 * q^61 - 96 * q^62 - 252 * q^63 + 32 * q^64 - 436 * q^65 - 296 * q^67 - 64 * q^68 - 156 * q^69 - 144 * q^70 - 244 * q^71 - 16 * q^72 - 200 * q^73 - 48 * q^74 - 232 * q^75 - 32 * q^76 - 168 * q^77 - 112 * q^78 - 180 * q^79 - 240 * q^80 - 286 * q^81 - 320 * q^82 - 120 * q^83 - 384 * q^84 - 176 * q^85 - 368 * q^86 - 116 * q^87 - 320 * q^88 - 296 * q^89 - 448 * q^90 - 108 * q^91 - 320 * q^92 - 416 * q^93 - 352 * q^94 - 156 * q^95 - 432 * q^96 - 200 * q^97 - 432 * q^98 - 168 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1472))\)

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
1472.2.a	\(\chi_{1472}(1, \cdot)\)	1472.2.a.a	1	1
		1472.2.a.b	1
		1472.2.a.c	1
		1472.2.a.d	1
		1472.2.a.e	1
		1472.2.a.f	1
		1472.2.a.g	1
		1472.2.a.h	1
		1472.2.a.i	1
		1472.2.a.j	1
		1472.2.a.k	1
		1472.2.a.l	1
		1472.2.a.m	1
		1472.2.a.n	1
		1472.2.a.o	2
		1472.2.a.p	2
		1472.2.a.q	2
		1472.2.a.r	2
		1472.2.a.s	2
		1472.2.a.t	2
		1472.2.a.u	2
		1472.2.a.v	2
		1472.2.a.w	3
		1472.2.a.x	3
		1472.2.a.y	4
		1472.2.a.z	4
1472.2.b	\(\chi_{1472}(737, \cdot)\)	1472.2.b.a	6	1
		1472.2.b.b	6
		1472.2.b.c	16
		1472.2.b.d	16
1472.2.c	\(\chi_{1472}(1471, \cdot)\)	1472.2.c.a	4	1
		1472.2.c.b	4
		1472.2.c.c	6
		1472.2.c.d	8
		1472.2.c.e	24
1472.2.h	\(\chi_{1472}(735, \cdot)\)	1472.2.h.a	8	1
		1472.2.h.b	8
		1472.2.h.c	32
1472.2.i	\(\chi_{1472}(367, \cdot)\)	1472.2.i.a	12	2
		1472.2.i.b	80
1472.2.j	\(\chi_{1472}(369, \cdot)\)	1472.2.j.a	2	2
		1472.2.j.b	4
		1472.2.j.c	12
		1472.2.j.d	24
		1472.2.j.e	46
1472.2.m	\(\chi_{1472}(185, \cdot)\)	None	0	4
1472.2.n	\(\chi_{1472}(183, \cdot)\)	None	0	4
1472.2.q	\(\chi_{1472}(193, \cdot)\)	n/a	460	10
1472.2.r	\(\chi_{1472}(93, \cdot)\)	n/a	1408	8
1472.2.u	\(\chi_{1472}(91, \cdot)\)	n/a	1520	8
1472.2.v	\(\chi_{1472}(159, \cdot)\)	n/a	480	10
1472.2.ba	\(\chi_{1472}(63, \cdot)\)	n/a	460	10
1472.2.bb	\(\chi_{1472}(225, \cdot)\)	n/a	480	10
1472.2.be	\(\chi_{1472}(49, \cdot)\)	n/a	920	20
1472.2.bf	\(\chi_{1472}(15, \cdot)\)	n/a	920	20
1472.2.bi	\(\chi_{1472}(7, \cdot)\)	None	0	40
1472.2.bj	\(\chi_{1472}(9, \cdot)\)	None	0	40
1472.2.bk	\(\chi_{1472}(11, \cdot)\)	n/a	15200	80
1472.2.bn	\(\chi_{1472}(13, \cdot)\)	n/a	15200	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1472))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1472)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(736))\)\(^{\oplus 2}\)