Space of modular forms of level 98 and weight 16

• Label: 98.16
• Level: 98
• Weight: 16
• Dimension: 1411
• Nonzero newspaces: 4
• Sturm bound: 9408
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(9408\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(98))\).

	Total	New	Old
Modular forms	4470	1411	3059
Cusp forms	4350	1411	2939
Eisenstein series	120	0	120

Trace form

1411 * q - 128 * q^2 - 11244 * q^3 + 16384 * q^4 - 843522 * q^5 + 2558976 * q^6 - 6429648 * q^7 - 2097152 * q^8 + 20916177 * q^9 - 114292992 * q^10 + 220797024 * q^11 - 184221696 * q^12 + 1689418274 * q^13 + 192656640 * q^14 - 4897994016 * q^15 + 268435456 * q^16 + 12227454942 * q^17 - 16924993152 * q^18 + 6933074180 * q^19 + 16842915840 * q^20 - 25283203440 * q^21 - 48797781504 * q^22 + 40343391732 * q^23 + 47160754176 * q^24 - 174451986365 * q^25 - 141734799616 * q^26 + 323863188984 * q^27 - 51659636736 * q^28 - 246969695754 * q^29 + 571177227264 * q^30 - 706240590676 * q^31 - 34359738368 * q^32 + 596986402452 * q^33 + 1434104648448 * q^34 + 254173040940 * q^35 - 5837923663872 * q^36 + 1356700497002 * q^37 + 530526810368 * q^38 - 5609202252636 * q^39 + 4017094656000 * q^40 + 14791170487530 * q^41 - 15593232731904 * q^42 - 8476132421692 * q^43 + 5276453339136 * q^44 + 55079167583946 * q^45 + 16058699483904 * q^46 + 23365380504876 * q^47 - 4192424951808 * q^48 - 44062183241070 * q^49 - 13032389808512 * q^50 + 169797724527708 * q^51 + 15002526089216 * q^52 - 127287230630382 * q^53 - 180684239351040 * q^54 + 23740007677956 * q^55 + 41851646115840 * q^56 + 132912864369696 * q^57 - 25391066544384 * q^58 - 345333520673604 * q^59 - 126993040441344 * q^60 + 409663916210414 * q^61 + 240693526343936 * q^62 - 396712950936576 * q^63 - 259484744155136 * q^64 - 547784896725948 * q^65 - 436182185601024 * q^66 - 193268366693152 * q^67 + 200334621769728 * q^68 + 982299403276776 * q^69 + 195443614308096 * q^70 - 67780356910200 * q^71 - 277299087802368 * q^72 - 1722763511181394 * q^73 + 415402842152192 * q^74 + 1850122156806912 * q^75 + 358042587103232 * q^76 + 417663644694702 * q^77 - 218721626944512 * q^78 - 1994871601903108 * q^79 - 226431212716032 * q^80 + 1153508407737117 * q^81 + 1422290936411904 * q^82 + 1668832470627564 * q^83 + 471914839080960 * q^84 - 2151536809875144 * q^85 - 992924803724800 * q^86 - 2249928352556256 * q^87 - 1020902913343488 * q^88 + 465017063991450 * q^89 + 9338953487303424 * q^90 + 2618963705562138 * q^91 - 1483113119612928 * q^92 + 463440893598552 * q^93 - 3920779735827456 * q^94 + 294737896608708 * q^95 + 772681796419584 * q^96 + 4051228093628270 * q^97 + 829675693676544 * q^98 + 3305993484419748 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(98))\)

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
98.16.a	\(\chi_{98}(1, \cdot)\)	98.16.a.a	1	1
		98.16.a.b	1
		98.16.a.c	2
		98.16.a.d	2
		98.16.a.e	3
		98.16.a.f	4
		98.16.a.g	4
		98.16.a.h	5
		98.16.a.i	5
		98.16.a.j	5
		98.16.a.k	5
		98.16.a.l	6
		98.16.a.m	8
98.16.c	\(\chi_{98}(67, \cdot)\)	98.16.c.a	2	2
		98.16.c.b	2
		98.16.c.c	2
		98.16.c.d	2
		98.16.c.e	4
		98.16.c.f	4
		98.16.c.g	4
		98.16.c.h	4
		98.16.c.i	6
		98.16.c.j	6
		98.16.c.k	8
		98.16.c.l	8
		98.16.c.m	10
		98.16.c.n	10
		98.16.c.o	12
		98.16.c.p	16
98.16.e	\(\chi_{98}(15, \cdot)\)	n/a	420	6
98.16.g	\(\chi_{98}(9, \cdot)\)	n/a	840	12

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(98)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)