Space of modular forms of level 1104 and weight 2

• Label: 1104.2
• Level: 1104
• Weight: 2
• Dimension: 14012
• Nonzero newspaces: 16
• Sturm bound: 135168
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(135168\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1104))\).

	Total	New	Old
Modular forms	35024	14392	20632
Cusp forms	32561	14012	18549
Eisenstein series	2463	380	2083

Trace form

14012 * q - 31 * q^3 - 72 * q^4 + 4 * q^5 - 28 * q^6 - 50 * q^7 + 24 * q^8 - q^9 - 72 * q^10 + 24 * q^11 - 44 * q^12 - 90 * q^13 - 24 * q^14 - 13 * q^15 - 120 * q^16 - 4 * q^17 - 60 * q^18 - 34 * q^19 - 32 * q^20 - 63 * q^21 - 120 * q^22 - 8 * q^23 - 144 * q^24 - 40 * q^25 - 40 * q^26 - 55 * q^27 - 88 * q^28 + 20 * q^29 - 84 * q^30 - 98 * q^31 - 83 * q^33 - 72 * q^34 - 48 * q^35 - 76 * q^36 - 42 * q^37 + 16 * q^38 - 69 * q^39 - 40 * q^40 + 12 * q^41 + 44 * q^42 - 66 * q^43 + 80 * q^44 - 16 * q^45 - 40 * q^46 + 84 * q^48 - 108 * q^49 + 72 * q^50 - 101 * q^51 - 24 * q^52 - 28 * q^53 + 52 * q^54 - 130 * q^55 + 5 * q^57 - 120 * q^58 - 56 * q^59 - 60 * q^60 - 218 * q^61 + 24 * q^62 - 49 * q^63 - 216 * q^64 + 24 * q^65 - 148 * q^66 - 98 * q^67 - 64 * q^68 - 83 * q^69 - 320 * q^70 + 16 * q^71 - 116 * q^72 - 82 * q^73 - 104 * q^74 + 71 * q^75 - 216 * q^76 + 56 * q^77 - 140 * q^78 + 98 * q^79 - 16 * q^80 + 63 * q^81 - 136 * q^82 + 204 * q^83 - 28 * q^84 + 130 * q^85 + 32 * q^86 + 273 * q^87 - 24 * q^88 + 188 * q^89 + 4 * q^90 + 304 * q^91 + 16 * q^92 + 54 * q^93 - 8 * q^94 + 376 * q^95 + 68 * q^96 + 46 * q^97 + 80 * q^98 + 293 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1104))\)

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
1104.2.a	\(\chi_{1104}(1, \cdot)\)	1104.2.a.a	1	1
		1104.2.a.b	1
		1104.2.a.c	1
		1104.2.a.d	1
		1104.2.a.e	1
		1104.2.a.f	1
		1104.2.a.g	1
		1104.2.a.h	1
		1104.2.a.i	1
		1104.2.a.j	2
		1104.2.a.k	2
		1104.2.a.l	2
		1104.2.a.m	2
		1104.2.a.n	2
		1104.2.a.o	3
1104.2.b	\(\chi_{1104}(137, \cdot)\)	None	0	1
1104.2.e	\(\chi_{1104}(47, \cdot)\)	1104.2.e.a	2	1
		1104.2.e.b	2
		1104.2.e.c	4
		1104.2.e.d	4
		1104.2.e.e	8
		1104.2.e.f	8
		1104.2.e.g	8
		1104.2.e.h	8
1104.2.f	\(\chi_{1104}(553, \cdot)\)	None	0	1
1104.2.i	\(\chi_{1104}(367, \cdot)\)	1104.2.i.a	8	1
		1104.2.i.b	16
1104.2.j	\(\chi_{1104}(599, \cdot)\)	None	0	1
1104.2.m	\(\chi_{1104}(689, \cdot)\)	1104.2.m.a	6	1
		1104.2.m.b	8
		1104.2.m.c	8
		1104.2.m.d	8
		1104.2.m.e	16
1104.2.n	\(\chi_{1104}(919, \cdot)\)	None	0	1
1104.2.q	\(\chi_{1104}(91, \cdot)\)	n/a	192	2
1104.2.t	\(\chi_{1104}(277, \cdot)\)	n/a	176	2
1104.2.u	\(\chi_{1104}(323, \cdot)\)	n/a	352	2
1104.2.x	\(\chi_{1104}(413, \cdot)\)	n/a	376	2
1104.2.y	\(\chi_{1104}(49, \cdot)\)	n/a	240	10
1104.2.bb	\(\chi_{1104}(7, \cdot)\)	None	0	10
1104.2.bc	\(\chi_{1104}(17, \cdot)\)	n/a	460	10
1104.2.bf	\(\chi_{1104}(71, \cdot)\)	None	0	10
1104.2.bg	\(\chi_{1104}(79, \cdot)\)	n/a	240	10
1104.2.bj	\(\chi_{1104}(25, \cdot)\)	None	0	10
1104.2.bk	\(\chi_{1104}(95, \cdot)\)	n/a	480	10
1104.2.bn	\(\chi_{1104}(89, \cdot)\)	None	0	10
1104.2.bo	\(\chi_{1104}(5, \cdot)\)	n/a	3760	20
1104.2.br	\(\chi_{1104}(35, \cdot)\)	n/a	3760	20
1104.2.bs	\(\chi_{1104}(13, \cdot)\)	n/a	1920	20
1104.2.bv	\(\chi_{1104}(19, \cdot)\)	n/a	1920	20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1104))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1104)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 2}\)