Space of modular forms of level 1472 and weight 4

• Label: 1472.4
• Level: 1472
• Weight: 4
• Dimension: 113154
• Nonzero newspaces: 16
• Sturm bound: 540672
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(540672\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1472))\).

	Total	New	Old
Modular forms	204336	114078	90258
Cusp forms	201168	113154	88014
Eisenstein series	3168	924	2244

Trace form

113154 * q - 160 * q^2 - 120 * q^3 - 160 * q^4 - 160 * q^5 - 160 * q^6 - 116 * q^7 - 160 * q^8 - 146 * q^9 - 160 * q^10 - 80 * q^11 - 160 * q^12 - 304 * q^13 - 160 * q^14 - 364 * q^15 - 160 * q^16 - 488 * q^17 - 160 * q^18 - 168 * q^19 - 160 * q^20 - 136 * q^21 - 1104 * q^22 - 124 * q^23 - 2336 * q^24 - 302 * q^25 - 80 * q^26 + 252 * q^27 + 1360 * q^28 + 640 * q^29 + 4480 * q^30 + 604 * q^31 + 2320 * q^32 + 1844 * q^33 + 1840 * q^34 + 836 * q^35 + 1600 * q^36 + 880 * q^37 - 1040 * q^38 - 116 * q^39 - 3440 * q^40 - 2248 * q^41 - 6480 * q^42 - 1792 * q^43 - 2160 * q^44 - 3128 * q^45 - 168 * q^46 - 2136 * q^47 - 160 * q^48 - 2406 * q^49 + 5552 * q^50 - 9068 * q^51 + 6464 * q^52 - 976 * q^53 + 3296 * q^54 - 1268 * q^55 - 944 * q^56 + 1956 * q^57 - 4912 * q^58 + 8800 * q^59 - 9952 * q^60 + 2000 * q^61 - 6144 * q^62 + 15236 * q^63 - 12256 * q^64 + 4108 * q^65 - 11232 * q^66 + 11928 * q^67 - 4288 * q^68 + 468 * q^69 - 4368 * q^70 + 780 * q^71 + 1136 * q^72 - 2248 * q^73 + 5104 * q^74 - 14856 * q^75 + 11744 * q^76 - 6408 * q^77 + 3824 * q^78 - 20276 * q^79 - 8688 * q^80 - 13918 * q^81 - 14080 * q^82 - 5240 * q^83 - 8448 * q^84 - 3472 * q^85 + 880 * q^86 - 116 * q^87 + 6080 * q^88 + 6936 * q^89 + 18560 * q^90 + 6548 * q^91 + 12448 * q^92 + 16416 * q^93 + 17696 * q^94 + 13668 * q^95 + 25680 * q^96 + 18584 * q^97 + 24048 * q^98 + 9368 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1472))\)

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
1472.4.a	\(\chi_{1472}(1, \cdot)\)	1472.4.a.a	1	1
		1472.4.a.b	1
		1472.4.a.c	1
		1472.4.a.d	1
		1472.4.a.e	1
		1472.4.a.f	1
		1472.4.a.g	1
		1472.4.a.h	1
		1472.4.a.i	1
		1472.4.a.j	1
		1472.4.a.k	2
		1472.4.a.l	2
		1472.4.a.m	2
		1472.4.a.n	2
		1472.4.a.o	3
		1472.4.a.p	3
		1472.4.a.q	3
		1472.4.a.r	3
		1472.4.a.s	3
		1472.4.a.t	3
		1472.4.a.u	3
		1472.4.a.v	3
		1472.4.a.w	3
		1472.4.a.x	3
		1472.4.a.y	4
		1472.4.a.z	4
		1472.4.a.ba	4
		1472.4.a.bb	4
		1472.4.a.bc	4
		1472.4.a.bd	4
		1472.4.a.be	4
		1472.4.a.bf	4
		1472.4.a.bg	8
		1472.4.a.bh	8
		1472.4.a.bi	9
		1472.4.a.bj	9
		1472.4.a.bk	9
		1472.4.a.bl	9
1472.4.b	\(\chi_{1472}(737, \cdot)\)	n/a	132	1
1472.4.c	\(\chi_{1472}(1471, \cdot)\)	n/a	142	1
1472.4.h	\(\chi_{1472}(735, \cdot)\)	n/a	144	1
1472.4.i	\(\chi_{1472}(367, \cdot)\)	n/a	284	2
1472.4.j	\(\chi_{1472}(369, \cdot)\)	n/a	264	2
1472.4.m	\(\chi_{1472}(185, \cdot)\)	None	0	4
1472.4.n	\(\chi_{1472}(183, \cdot)\)	None	0	4
1472.4.q	\(\chi_{1472}(193, \cdot)\)	n/a	1420	10
1472.4.r	\(\chi_{1472}(93, \cdot)\)	n/a	4224	8
1472.4.u	\(\chi_{1472}(91, \cdot)\)	n/a	4592	8
1472.4.v	\(\chi_{1472}(159, \cdot)\)	n/a	1440	10
1472.4.ba	\(\chi_{1472}(63, \cdot)\)	n/a	1420	10
1472.4.bb	\(\chi_{1472}(225, \cdot)\)	n/a	1440	10
1472.4.be	\(\chi_{1472}(49, \cdot)\)	n/a	2840	20
1472.4.bf	\(\chi_{1472}(15, \cdot)\)	n/a	2840	20
1472.4.bi	\(\chi_{1472}(7, \cdot)\)	None	0	40
1472.4.bj	\(\chi_{1472}(9, \cdot)\)	None	0	40
1472.4.bk	\(\chi_{1472}(11, \cdot)\)	n/a	45920	80
1472.4.bn	\(\chi_{1472}(13, \cdot)\)	n/a	45920	80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1472))\) into lower level spaces

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