Space of modular forms of level 704 and weight 5

• Label: 704.5
• Level: 704
• Weight: 5
• Dimension: 33786
• Nonzero newspaces: 16
• Sturm bound: 153600
• Trace bound: 9

Defining parameters

Level:	$N$	=	$704 = 2^{6} \cdot 11$
Weight:	$k$	=	$5$
Nonzero newspaces:			$16$
Sturm bound:			$153600$
Trace bound:			$9$

Dimensions

The following table gives the dimensions of various subspaces of $M_{5}(\Gamma_1(704))$.

	Total	New	Old
Modular forms	62160	34182	27978
Cusp forms	60720	33786	26934
Eisenstein series	1440	396	1044

Trace form

33786 * q - 64 * q^2 - 48 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 52 * q^7 - 64 * q^8 - 242 * q^9 - 64 * q^10 + 42 * q^11 - 144 * q^12 + 640 * q^13 - 64 * q^14 - 44 * q^15 - 64 * q^16 - 1072 * q^17 - 64 * q^18 - 1456 * q^19 - 64 * q^20 + 8 * q^21 + 2592 * q^22 + 2192 * q^23 + 496 * q^24 - 1518 * q^25 - 10864 * q^26 - 3372 * q^27 - 11344 * q^28 - 3520 * q^29 - 9504 * q^30 - 28 * q^31 + 4976 * q^32 + 3752 * q^33 + 14016 * q^34 + 2636 * q^35 + 37536 * q^36 + 3072 * q^37 + 15056 * q^38 + 5324 * q^39 - 784 * q^40 + 2992 * q^41 - 32624 * q^42 + 3344 * q^43 - 8496 * q^44 + 3112 * q^45 - 64 * q^46 - 44 * q^47 - 64 * q^48 - 1326 * q^49 - 43120 * q^50 + 26188 * q^51 - 18016 * q^52 - 20224 * q^53 + 31040 * q^54 - 35384 * q^55 + 49248 * q^56 - 19860 * q^57 + 65456 * q^58 - 57840 * q^59 + 63872 * q^60 + 16512 * q^61 + 12000 * q^62 - 60 * q^63 - 24448 * q^64 - 4396 * q^65 - 35624 * q^66 + 91412 * q^67 - 53344 * q^68 + 18824 * q^69 - 122368 * q^70 + 119756 * q^71 - 81712 * q^72 + 35760 * q^73 - 33328 * q^74 + 44312 * q^75 + 28224 * q^76 + 16732 * q^77 + 207744 * q^78 - 100396 * q^79 + 230000 * q^80 - 3318 * q^81 + 10336 * q^82 - 34608 * q^83 - 115872 * q^84 - 83456 * q^85 - 170416 * q^86 - 98592 * q^87 - 71192 * q^88 - 134196 * q^89 - 223264 * q^90 - 56116 * q^91 - 159664 * q^92 - 66736 * q^93 - 35968 * q^94 - 28 * q^95 + 51888 * q^96 + 85136 * q^97 + 152528 * q^98 + 48514 * q^99

Decomposition of $S_{5}^{\mathrm{new}}(\Gamma_1(704))$

We only show spaces with odd 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
704.5.b	$\chi_{704}(417, \cdot)$	704.5.b.a	4	1
		704.5.b.b	4
		704.5.b.c	8
		704.5.b.d	24
		704.5.b.e	56
704.5.d	$\chi_{704}(639, \cdot)$	704.5.d.a	2	1
		704.5.d.b	6
		704.5.d.c	12
		704.5.d.d	20
		704.5.d.e	20
		704.5.d.f	20
704.5.f	$\chi_{704}(287, \cdot)$	704.5.f.a	24	1
		704.5.f.b	56
704.5.h	$\chi_{704}(65, \cdot)$	704.5.h.a	1	1
		704.5.h.b	1
		704.5.h.c	2
		704.5.h.d	2
		704.5.h.e	2
		704.5.h.f	2
		704.5.h.g	2
		704.5.h.h	2
		704.5.h.i	4
		704.5.h.j	4
		704.5.h.k	12
		704.5.h.l	12
		704.5.h.m	24
		704.5.h.n	24
704.5.k	$\chi_{704}(111, \cdot)$	n/a	160	2
704.5.l	$\chi_{704}(241, \cdot)$	n/a	188	2
704.5.o	$\chi_{704}(153, \cdot)$	None	0	4
704.5.p	$\chi_{704}(23, \cdot)$	None	0	4
704.5.r	$\chi_{704}(129, \cdot)$	n/a	376	4
704.5.t	$\chi_{704}(31, \cdot)$	n/a	384	4
704.5.v	$\chi_{704}(191, \cdot)$	n/a	376	4
704.5.x	$\chi_{704}(161, \cdot)$	n/a	384	4
704.5.y	$\chi_{704}(21, \cdot)$	n/a	3056	8
704.5.ba	$\chi_{704}(67, \cdot)$	n/a	2560	8
704.5.bc	$\chi_{704}(17, \cdot)$	n/a	752	8
704.5.bd	$\chi_{704}(15, \cdot)$	n/a	752	8
704.5.bh	$\chi_{704}(71, \cdot)$	None	0	16
704.5.bi	$\chi_{704}(41, \cdot)$	None	0	16
704.5.bl	$\chi_{704}(3, \cdot)$	n/a	12224	32
704.5.bn	$\chi_{704}(13, \cdot)$	n/a	12224	32

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

Decomposition of $S_{5}^{\mathrm{old}}(\Gamma_1(704))$ into lower level spaces

$S_{5}^{\mathrm{old}}(\Gamma_1(704)) \cong$ $S_{5}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 14}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 12}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 10}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 8}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(11))$$^{\oplus 7}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 6}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(22))$$^{\oplus 6}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(32))$$^{\oplus 4}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(44))$$^{\oplus 5}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(64))$$^{\oplus 2}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(88))$$^{\oplus 4}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(176))$$^{\oplus 3}$$\oplus$$S_{5}^{\mathrm{new}}(\Gamma_1(352))$$^{\oplus 2}$