Space of modular forms of level 98 and weight 14

• Label: 98.14
• Level: 98
• Weight: 14
• Dimension: 1224
• Nonzero newspaces: 4
• Sturm bound: 8232
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(8232\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(98))\).

	Total	New	Old
Modular forms	3882	1224	2658
Cusp forms	3762	1224	2538
Eisenstein series	120	0	120

Trace form

1224 * q - 3516 * q^3 - 8192 * q^4 + 134688 * q^5 - 363264 * q^6 + 751288 * q^7 + 1746654 * q^9 + 9485568 * q^10 + 15616176 * q^11 - 14401536 * q^12 - 58880440 * q^13 - 67302528 * q^14 + 537220896 * q^15 - 33554432 * q^16 - 303900684 * q^17 + 721012224 * q^18 + 886029836 * q^19 - 986972160 * q^20 - 362014098 * q^21 + 2671750656 * q^22 - 238322976 * q^23 - 915406848 * q^24 - 632305574 * q^25 + 144169728 * q^26 + 28525645944 * q^27 - 276660224 * q^28 - 36621811476 * q^29 + 7409739264 * q^30 + 10229548280 * q^31 - 8843677968 * q^33 - 36400547328 * q^34 - 31492247682 * q^35 - 76008726528 * q^36 - 47778681788 * q^37 + 204148615296 * q^38 - 200643250158 * q^39 - 153503662080 * q^40 - 213108258936 * q^41 + 535217489280 * q^42 + 434239802852 * q^43 - 149381111808 * q^44 - 1457898510174 * q^45 - 340639809408 * q^46 + 239557758684 * q^47 + 112239575040 * q^48 + 1417308740014 * q^49 - 526276255488 * q^50 - 1734661805328 * q^51 + 186517282816 * q^52 + 25829355576 * q^53 + 1178383100544 * q^54 + 4573292339586 * q^55 + 655855976448 * q^56 - 315922134468 * q^57 - 1600207227648 * q^58 + 1159069346976 * q^59 + 974996250624 * q^60 + 4314815886850 * q^61 - 2538213156480 * q^62 - 12792267630276 * q^63 - 3435973836800 * q^64 + 11541454861104 * q^65 + 7945811927040 * q^66 + 2319966407912 * q^67 - 1244777201664 * q^68 - 21383941740768 * q^69 - 3277619624832 * q^70 + 2890912896864 * q^71 + 2953266069504 * q^72 + 16485815088716 * q^73 + 10751635284480 * q^74 - 19544622242580 * q^75 - 12077653049344 * q^76 - 10889074292628 * q^77 + 12546894225408 * q^78 + 28718883732752 * q^79 + 2259689668608 * q^80 + 14814195388890 * q^81 - 9900452488704 * q^82 - 7504778525616 * q^83 - 2376135450624 * q^84 - 25005927481260 * q^85 + 1949835044352 * q^86 + 93083719370496 * q^87 - 1196068700160 * q^88 - 6808552470384 * q^89 - 16570431373056 * q^90 - 34833679974586 * q^91 + 4536370593792 * q^92 - 92871645376548 * q^93 + 31149775911936 * q^94 - 17042668794264 * q^95 - 3749506449408 * q^96 + 58839371828744 * q^97 + 14367468688896 * q^98 + 56749764777768 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(98))\)

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
98.14.a	\(\chi_{98}(1, \cdot)\)	98.14.a.a	1	1
		98.14.a.b	1
		98.14.a.c	1
		98.14.a.d	1
		98.14.a.e	2
		98.14.a.f	2
		98.14.a.g	2
		98.14.a.h	4
		98.14.a.i	4
		98.14.a.j	4
		98.14.a.k	4
		98.14.a.l	4
		98.14.a.m	6
		98.14.a.n	8
98.14.c	\(\chi_{98}(67, \cdot)\)	98.14.c.a	2	2
		98.14.c.b	2
		98.14.c.c	2
		98.14.c.d	2
		98.14.c.e	2
		98.14.c.f	2
		98.14.c.g	2
		98.14.c.h	2
		98.14.c.i	4
		98.14.c.j	4
		98.14.c.k	4
		98.14.c.l	4
		98.14.c.m	4
		98.14.c.n	8
		98.14.c.o	8
		98.14.c.p	8
		98.14.c.q	12
		98.14.c.r	16
98.14.e	\(\chi_{98}(15, \cdot)\)	n/a	372	6
98.14.g	\(\chi_{98}(9, \cdot)\)	n/a	720	12

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces

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