Space of modular forms of level 110 and weight 4

• Label: 110.4
• Level: 110
• Weight: 4
• Dimension: 324
• Nonzero newspaces: 6
• Newform subspaces: 19
• Sturm bound: 2880
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(2880\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(110))\).

	Total	New	Old
Modular forms	1160	324	836
Cusp forms	1000	324	676
Eisenstein series	160	0	160

Trace form

324 * q - 4 * q^2 + 16 * q^3 + 8 * q^4 + 10 * q^5 - 84 * q^6 - 32 * q^7 - 16 * q^8 + 154 * q^9 + 244 * q^11 + 224 * q^12 + 196 * q^13 + 184 * q^14 - 250 * q^15 - 96 * q^16 - 752 * q^17 - 608 * q^18 + 410 * q^19 - 120 * q^20 + 568 * q^21 - 24 * q^22 - 1044 * q^23 - 208 * q^24 - 50 * q^25 - 264 * q^26 + 10 * q^27 + 272 * q^28 + 1040 * q^29 + 1020 * q^30 + 28 * q^31 + 256 * q^32 + 2626 * q^33 + 424 * q^34 + 10 * q^35 + 272 * q^36 + 548 * q^37 + 520 * q^38 - 512 * q^39 - 1752 * q^41 - 408 * q^42 + 796 * q^43 - 152 * q^44 + 2500 * q^45 + 656 * q^46 + 1148 * q^47 + 256 * q^48 - 154 * q^49 - 1340 * q^50 - 3762 * q^51 - 1456 * q^52 - 7204 * q^53 - 4800 * q^54 - 8610 * q^55 - 768 * q^56 - 7390 * q^57 - 3000 * q^58 - 1350 * q^59 - 1440 * q^60 - 6412 * q^61 - 3208 * q^62 + 456 * q^63 + 128 * q^64 + 7020 * q^65 + 816 * q^66 + 12648 * q^67 + 2112 * q^68 + 14128 * q^69 + 5640 * q^70 + 10128 * q^71 + 1648 * q^72 + 1016 * q^73 + 4824 * q^74 + 5270 * q^75 + 3280 * q^76 - 1212 * q^77 + 4064 * q^78 - 3040 * q^79 + 800 * q^80 - 5976 * q^81 - 1628 * q^82 - 9034 * q^83 - 3104 * q^84 - 520 * q^85 - 7924 * q^86 - 8240 * q^87 - 1216 * q^88 - 4280 * q^89 - 5520 * q^90 - 52 * q^91 + 2304 * q^92 + 9532 * q^93 + 5824 * q^94 + 12480 * q^95 + 256 * q^96 + 10118 * q^97 + 10128 * q^98 + 16624 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(110))\)

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
110.4.a	\(\chi_{110}(1, \cdot)\)	110.4.a.a	1	1
		110.4.a.b	1
		110.4.a.c	1
		110.4.a.d	1
		110.4.a.e	1
		110.4.a.f	1
		110.4.a.g	1
		110.4.a.h	1
		110.4.a.i	2
110.4.b	\(\chi_{110}(89, \cdot)\)	110.4.b.a	2	1
		110.4.b.b	4
		110.4.b.c	8
110.4.f	\(\chi_{110}(43, \cdot)\)	110.4.f.a	36	2
110.4.g	\(\chi_{110}(31, \cdot)\)	110.4.g.a	8	4
		110.4.g.b	12
		110.4.g.c	12
		110.4.g.d	16
110.4.j	\(\chi_{110}(9, \cdot)\)	110.4.j.a	72	4
110.4.k	\(\chi_{110}(7, \cdot)\)	110.4.k.a	144	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(110))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(110)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)