Space of modular forms of level 98 and weight 8

• Label: 98.8
• Level: 98
• Weight: 8
• Dimension: 659
• Nonzero newspaces: 4
• Newform subspaces: 30
• Sturm bound: 4704
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 30 \)
Sturm bound:			\(4704\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(98))\).

	Total	New	Old
Modular forms	2118	659	1459
Cusp forms	1998	659	1339
Eisenstein series	120	0	120

Trace form

659 * q - 8 * q^2 + 120 * q^3 - 192 * q^4 - 222 * q^5 + 2496 * q^6 + 664 * q^7 - 512 * q^8 - 9183 * q^9 + 2928 * q^10 + 15180 * q^11 + 7680 * q^12 - 44838 * q^13 + 26832 * q^14 - 2856 * q^15 - 12288 * q^16 - 210630 * q^17 + 2712 * q^18 + 139104 * q^19 + 82560 * q^20 + 174918 * q^21 + 8736 * q^22 - 371832 * q^23 - 184320 * q^24 - 434085 * q^25 + 170096 * q^26 + 1116864 * q^27 - 11264 * q^28 + 108774 * q^29 - 1039296 * q^30 - 1091304 * q^31 - 32768 * q^32 + 2156856 * q^33 + 825648 * q^34 + 56910 * q^35 - 996288 * q^36 - 498562 * q^37 - 3275632 * q^38 - 8360766 * q^39 - 92160 * q^40 + 5145582 * q^41 + 5768208 * q^42 + 3949632 * q^43 + 3006336 * q^44 + 4833876 * q^45 - 4435920 * q^46 - 12143460 * q^47 - 1056768 * q^48 - 17608886 * q^49 + 1702888 * q^50 + 10539432 * q^51 + 2544896 * q^52 + 11880594 * q^53 + 11361456 * q^54 + 7454226 * q^55 + 5179392 * q^56 + 4292844 * q^57 - 6551184 * q^58 - 6864804 * q^59 - 5537664 * q^60 - 31612132 * q^61 + 7869584 * q^62 + 37224732 * q^63 - 7077888 * q^64 + 10757292 * q^65 - 3772032 * q^66 - 10719540 * q^67 - 13480320 * q^68 - 15785136 * q^69 - 14363664 * q^70 - 9868824 * q^71 + 173568 * q^72 - 1026294 * q^73 + 11980496 * q^74 + 51106392 * q^75 + 25589760 * q^76 + 15014832 * q^77 + 21462720 * q^78 - 36425424 * q^79 - 909312 * q^80 - 43093911 * q^81 - 39522960 * q^82 - 46932684 * q^83 - 13975680 * q^84 - 31830624 * q^85 - 43612768 * q^86 + 31600968 * q^87 + 11126784 * q^88 + 142772694 * q^89 + 132569904 * q^90 + 76722398 * q^91 + 18826752 * q^92 - 34877316 * q^93 - 47118144 * q^94 - 219103152 * q^95 - 11796480 * q^96 - 154649058 * q^97 - 31638144 * q^98 - 182230524 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(98))\)

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
98.8.a	\(\chi_{98}(1, \cdot)\)	98.8.a.a	1	1
		98.8.a.b	1
		98.8.a.c	1
		98.8.a.d	2
		98.8.a.e	2
		98.8.a.f	2
		98.8.a.g	2
		98.8.a.h	2
		98.8.a.i	2
		98.8.a.j	2
		98.8.a.k	2
		98.8.a.l	4
98.8.c	\(\chi_{98}(67, \cdot)\)	98.8.c.a	2	2
		98.8.c.b	2
		98.8.c.c	2
		98.8.c.d	2
		98.8.c.e	2
		98.8.c.f	2
		98.8.c.g	4
		98.8.c.h	4
		98.8.c.i	4
		98.8.c.j	4
		98.8.c.k	4
		98.8.c.l	4
		98.8.c.m	4
		98.8.c.n	8
98.8.e	\(\chi_{98}(15, \cdot)\)	98.8.e.a	102	6
		98.8.e.b	102
98.8.g	\(\chi_{98}(9, \cdot)\)	98.8.g.a	192	12
		98.8.g.b	192

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(98)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)