Space of modular forms of level 88 and weight 3

• Label: 88.3
• Level: 88
• Weight: 3
• Dimension: 248
• Nonzero newspaces: 6
• Newform subspaces: 9
• Sturm bound: 1440
• Trace bound: 2

Defining parameters

Level:	$N$	=	$88 = 2^{3} \cdot 11$
Weight:	$k$	=	$3$
Nonzero newspaces:			$6$
Newform subspaces:			$9$
Sturm bound:			$1440$
Trace bound:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(\Gamma_1(88))$.

	Total	New	Old
Modular forms	540	284	256
Cusp forms	420	248	172
Eisenstein series	120	36	84

Trace form

248 * q - 6 * q^2 - 6 * q^3 - 18 * q^4 - 18 * q^6 - 10 * q^7 + 6 * q^8 - 10 * q^9 - 10 * q^10 - 24 * q^11 - 4 * q^12 - 10 * q^14 + 50 * q^15 - 42 * q^16 + 16 * q^17 - 30 * q^18 + 88 * q^19 - 10 * q^20 + 18 * q^22 - 40 * q^23 - 42 * q^24 - 150 * q^25 - 10 * q^26 - 156 * q^27 - 10 * q^28 - 80 * q^29 - 100 * q^30 - 110 * q^31 - 56 * q^32 - 142 * q^33 - 372 * q^34 - 250 * q^35 - 530 * q^36 - 396 * q^38 - 250 * q^39 - 220 * q^40 + 12 * q^41 - 120 * q^42 - 48 * q^43 + 4 * q^44 + 60 * q^45 + 200 * q^46 + 110 * q^47 + 604 * q^48 + 62 * q^49 + 580 * q^50 + 548 * q^51 + 440 * q^52 + 240 * q^53 + 982 * q^54 + 550 * q^55 + 500 * q^56 + 374 * q^57 + 140 * q^58 + 364 * q^59 + 240 * q^60 + 80 * q^61 - 10 * q^62 - 20 * q^63 - 138 * q^64 - 20 * q^65 - 66 * q^66 - 224 * q^67 - 26 * q^68 - 160 * q^69 + 480 * q^70 - 570 * q^71 + 660 * q^72 - 316 * q^73 + 640 * q^74 - 1220 * q^75 + 1142 * q^76 - 780 * q^77 + 1060 * q^78 - 1090 * q^79 + 760 * q^80 - 588 * q^81 + 306 * q^82 - 816 * q^83 + 350 * q^84 - 120 * q^85 + 86 * q^86 - 58 * q^88 - 272 * q^89 - 450 * q^90 + 650 * q^91 - 410 * q^92 + 840 * q^93 - 850 * q^94 + 1070 * q^95 - 1128 * q^96 + 978 * q^97 - 1024 * q^98 + 1760 * q^99

Decomposition of $S_{3}^{\mathrm{new}}(\Gamma_1(88))$

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
88.3.b	$\chi_{88}(21, \cdot)$	88.3.b.a	1	1
		88.3.b.b	1
		88.3.b.c	20
88.3.d	$\chi_{88}(23, \cdot)$	None	0	1
88.3.f	$\chi_{88}(67, \cdot)$	88.3.f.a	20	1
88.3.h	$\chi_{88}(65, \cdot)$	88.3.h.a	6	1
88.3.j	$\chi_{88}(17, \cdot)$	88.3.j.a	24	4
88.3.l	$\chi_{88}(3, \cdot)$	88.3.l.a	8	4
		88.3.l.b	80
88.3.n	$\chi_{88}(15, \cdot)$	None	0	4
88.3.p	$\chi_{88}(13, \cdot)$	88.3.p.a	88	4

Decomposition of $S_{3}^{\mathrm{old}}(\Gamma_1(88))$ into lower level spaces

$S_{3}^{\mathrm{old}}(\Gamma_1(88)) \cong$ $S_{3}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 8}$$\oplus$$S_{3}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 6}$$\oplus$$S_{3}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 4}$$\oplus$$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 2}$$\oplus$$S_{3}^{\mathrm{new}}(\Gamma_1(11))$$^{\oplus 4}$$\oplus$$S_{3}^{\mathrm{new}}(\Gamma_1(22))$$^{\oplus 3}$$\oplus$$S_{3}^{\mathrm{new}}(\Gamma_1(44))$$^{\oplus 2}$