Space of modular forms of level 2106 and weight 2

• Label: 2106.2
• Level: 2106
• Weight: 2
• Dimension: 31872
• Nonzero newspaces: 33
• Sturm bound: 489888
• Trace bound: 45

Defining parameters

Level:	\( N \)	=	\( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 33 \)
Sturm bound:			\(489888\)
Trace bound:			\(45\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2106))\).

	Total	New	Old
Modular forms	125064	31872	93192
Cusp forms	119881	31872	88009
Eisenstein series	5183	0	5183

Trace form

31872 * q - 12 * q^5 - 12 * q^7 - 6 * q^8 - 12 * q^10 - 30 * q^11 - 12 * q^13 - 12 * q^14 - 24 * q^17 + 18 * q^18 + 36 * q^19 + 60 * q^20 + 108 * q^21 + 42 * q^22 + 156 * q^23 + 72 * q^25 + 90 * q^26 + 108 * q^27 + 48 * q^28 + 168 * q^29 + 108 * q^30 + 72 * q^31 + 108 * q^33 + 30 * q^34 + 120 * q^35 + 36 * q^36 + 12 * q^37 - 6 * q^38 - 12 * q^40 + 6 * q^41 - 18 * q^43 - 12 * q^44 + 108 * q^45 - 24 * q^46 + 108 * q^47 + 24 * q^49 - 72 * q^50 + 126 * q^51 - 12 * q^52 + 60 * q^53 + 72 * q^55 - 12 * q^56 + 108 * q^57 - 48 * q^58 + 138 * q^59 + 36 * q^61 - 48 * q^62 + 108 * q^63 - 6 * q^64 - 12 * q^65 - 144 * q^66 + 90 * q^67 - 60 * q^68 - 252 * q^69 + 48 * q^70 - 240 * q^71 - 144 * q^72 - 84 * q^73 - 228 * q^74 - 360 * q^75 + 30 * q^76 - 492 * q^77 - 144 * q^78 + 120 * q^79 - 48 * q^80 - 288 * q^81 - 12 * q^82 - 288 * q^83 - 72 * q^84 + 72 * q^85 - 234 * q^86 - 576 * q^87 + 42 * q^88 - 348 * q^89 - 288 * q^90 - 30 * q^91 - 132 * q^92 - 252 * q^93 + 36 * q^94 - 168 * q^95 - 36 * q^96 + 102 * q^97 - 30 * q^98 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2106))\)

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
2106.2.a	\(\chi_{2106}(1, \cdot)\)	2106.2.a.a	1	1
		2106.2.a.b	1
		2106.2.a.c	1
		2106.2.a.d	1
		2106.2.a.e	1
		2106.2.a.f	1
		2106.2.a.g	2
		2106.2.a.h	2
		2106.2.a.i	2
		2106.2.a.j	2
		2106.2.a.k	2
		2106.2.a.l	2
		2106.2.a.m	2
		2106.2.a.n	2
		2106.2.a.o	2
		2106.2.a.p	2
		2106.2.a.q	3
		2106.2.a.r	3
		2106.2.a.s	4
		2106.2.a.t	4
		2106.2.a.u	4
		2106.2.a.v	4
2106.2.b	\(\chi_{2106}(649, \cdot)\)	2106.2.b.a	6	1
		2106.2.b.b	6
		2106.2.b.c	14
		2106.2.b.d	14
		2106.2.b.e	16
2106.2.e	\(\chi_{2106}(703, \cdot)\)	2106.2.e.a	2	2
		2106.2.e.b	2
		2106.2.e.c	2
		2106.2.e.d	2
		2106.2.e.e	2
		2106.2.e.f	2
		2106.2.e.g	2
		2106.2.e.h	2
		2106.2.e.i	2
		2106.2.e.j	2
		2106.2.e.k	2
		2106.2.e.l	2
		2106.2.e.m	2
		2106.2.e.n	2
		2106.2.e.o	2
		2106.2.e.p	2
		2106.2.e.q	2
		2106.2.e.r	2
		2106.2.e.s	2
		2106.2.e.t	2
		2106.2.e.u	2
		2106.2.e.v	2
		2106.2.e.w	2
		2106.2.e.x	2
		2106.2.e.y	2
		2106.2.e.z	2
		2106.2.e.ba	2
		2106.2.e.bb	2
		2106.2.e.bc	4
		2106.2.e.bd	4
		2106.2.e.be	4
		2106.2.e.bf	4
		2106.2.e.bg	4
		2106.2.e.bh	4
		2106.2.e.bi	8
		2106.2.e.bj	8
2106.2.f	\(\chi_{2106}(55, \cdot)\)	n/a	112	2
2106.2.g	\(\chi_{2106}(217, \cdot)\)	n/a	112	2
2106.2.h	\(\chi_{2106}(1459, \cdot)\)	n/a	112	2
2106.2.j	\(\chi_{2106}(161, \cdot)\)	n/a	112	2
2106.2.l	\(\chi_{2106}(1135, \cdot)\)	n/a	112	2
2106.2.p	\(\chi_{2106}(595, \cdot)\)	n/a	112	2
2106.2.s	\(\chi_{2106}(433, \cdot)\)	n/a	112	2
2106.2.t	\(\chi_{2106}(1351, \cdot)\)	n/a	112	2
2106.2.w	\(\chi_{2106}(235, \cdot)\)	n/a	216	6
2106.2.x	\(\chi_{2106}(451, \cdot)\)	n/a	252	6
2106.2.y	\(\chi_{2106}(289, \cdot)\)	n/a	252	6
2106.2.ba	\(\chi_{2106}(323, \cdot)\)	n/a	224	4
2106.2.bb	\(\chi_{2106}(215, \cdot)\)	n/a	224	4
2106.2.bc	\(\chi_{2106}(917, \cdot)\)	n/a	224	4
2106.2.bg	\(\chi_{2106}(593, \cdot)\)	n/a	224	4
2106.2.bj	\(\chi_{2106}(361, \cdot)\)	n/a	252	6
2106.2.bk	\(\chi_{2106}(181, \cdot)\)	n/a	252	6
2106.2.bp	\(\chi_{2106}(127, \cdot)\)	n/a	252	6
2106.2.bq	\(\chi_{2106}(61, \cdot)\)	n/a	2268	18
2106.2.br	\(\chi_{2106}(79, \cdot)\)	n/a	1944	18
2106.2.bs	\(\chi_{2106}(133, \cdot)\)	n/a	2268	18
2106.2.bu	\(\chi_{2106}(305, \cdot)\)	n/a	504	12
2106.2.bv	\(\chi_{2106}(125, \cdot)\)	n/a	504	12
2106.2.by	\(\chi_{2106}(71, \cdot)\)	n/a	504	12
2106.2.bz	\(\chi_{2106}(25, \cdot)\)	n/a	2268	18
2106.2.ca	\(\chi_{2106}(43, \cdot)\)	n/a	2268	18
2106.2.cb	\(\chi_{2106}(121, \cdot)\)	n/a	2268	18
2106.2.cl	\(\chi_{2106}(5, \cdot)\)	n/a	4536	36
2106.2.cm	\(\chi_{2106}(41, \cdot)\)	n/a	4536	36
2106.2.cn	\(\chi_{2106}(11, \cdot)\)	n/a	4536	36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2106))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2106)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(702))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1053))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2106))\)\(^{\oplus 1}\)