Space of modular forms of level 98 and weight 7

• Label: 98.7
• Level: 98
• Weight: 7
• Dimension: 564
• Nonzero newspaces: 4
• Newform subspaces: 9
• Sturm bound: 4116
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(4116\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(98))\).

	Total	New	Old
Modular forms	1824	564	1260
Cusp forms	1704	564	1140
Eisenstein series	120	0	120

Trace form

564 * q + 672 * q^5 - 960 * q^7 - 3696 * q^9 + 4032 * q^10 + 11592 * q^11 - 4752 * q^14 - 45648 * q^15 + 34608 * q^17 + 33600 * q^18 + 64008 * q^19 - 29244 * q^21 - 53568 * q^22 - 72912 * q^23 - 21504 * q^24 + 72072 * q^25 + 9408 * q^26 - 2304 * q^28 + 97152 * q^29 + 65184 * q^30 + 6216 * q^31 - 6552 * q^33 - 14028 * q^35 + 26880 * q^36 - 458808 * q^37 + 53424 * q^38 + 714840 * q^39 + 322560 * q^40 + 348096 * q^41 - 36864 * q^42 - 102096 * q^43 - 174720 * q^44 - 2513448 * q^45 - 1097712 * q^46 - 1168776 * q^47 + 1455180 * q^49 + 321120 * q^50 + 2225160 * q^51 - 228480 * q^52 + 521640 * q^53 + 942480 * q^54 + 1023120 * q^55 - 239616 * q^56 - 524400 * q^57 - 590688 * q^58 - 1537200 * q^59 - 379008 * q^60 + 64344 * q^61 + 787920 * q^62 + 3808272 * q^63 - 786432 * q^64 - 2603832 * q^65 - 3346560 * q^66 - 428064 * q^67 - 1107456 * q^68 + 470736 * q^70 + 522960 * q^71 + 1075200 * q^72 + 3234168 * q^73 + 4279296 * q^74 + 4084416 * q^75 - 1146600 * q^77 - 4848384 * q^78 - 4326000 * q^79 - 688128 * q^80 - 4907784 * q^81 - 133056 * q^82 + 7043064 * q^83 + 509952 * q^84 + 6454944 * q^85 + 5815488 * q^86 + 7630392 * q^87 + 709632 * q^88 - 4888632 * q^89 - 7693920 * q^91 - 3125760 * q^92 - 22356936 * q^93 - 7590240 * q^94 - 9662016 * q^95 + 688128 * q^96 + 2704416 * q^98 + 21268272 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(98))\)

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
98.7.b	\(\chi_{98}(97, \cdot)\)	98.7.b.a	4	1
		98.7.b.b	8
		98.7.b.c	8
98.7.d	\(\chi_{98}(19, \cdot)\)	98.7.d.a	8	2
		98.7.d.b	8
		98.7.d.c	8
		98.7.d.d	16
98.7.f	\(\chi_{98}(13, \cdot)\)	98.7.f.a	168	6
98.7.h	\(\chi_{98}(3, \cdot)\)	98.7.h.a	336	12

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces

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