Space of modular forms of level 165 and weight 4

• Label: 165.4
• Level: 165
• Weight: 4
• Dimension: 1892
• Nonzero newspaces: 12
• Newform subspaces: 26
• Sturm bound: 7680
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(7680\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(165))\).

	Total	New	Old
Modular forms	3040	1996	1044
Cusp forms	2720	1892	828
Eisenstein series	320	104	216

Trace form

1892 * q - 8 * q^2 + 2 * q^3 + 28 * q^4 - 12 * q^5 - 130 * q^6 - 20 * q^7 + 232 * q^8 + 186 * q^9 + 352 * q^10 + 256 * q^11 + 84 * q^12 - 268 * q^13 - 1308 * q^14 - 673 * q^15 - 2188 * q^16 - 680 * q^17 + 118 * q^18 + 1392 * q^19 + 1822 * q^20 + 1976 * q^21 + 3020 * q^22 + 1336 * q^23 + 2586 * q^24 + 158 * q^25 - 364 * q^26 - 1474 * q^27 - 3512 * q^28 - 2976 * q^29 - 4182 * q^30 - 4084 * q^31 - 3792 * q^32 - 3608 * q^33 - 2664 * q^34 - 120 * q^35 - 1078 * q^36 + 2580 * q^37 + 2084 * q^38 + 3378 * q^39 + 4364 * q^40 + 5168 * q^41 + 8364 * q^42 + 5616 * q^43 + 9772 * q^44 + 2388 * q^45 + 5616 * q^46 + 2136 * q^47 + 3760 * q^48 - 1160 * q^49 - 2818 * q^50 - 412 * q^51 - 10888 * q^52 - 7104 * q^53 - 648 * q^54 - 10046 * q^55 - 17360 * q^56 - 7532 * q^57 - 10192 * q^58 - 3032 * q^59 - 8202 * q^60 - 6532 * q^61 - 5824 * q^62 - 10334 * q^63 - 2948 * q^64 + 1984 * q^65 - 9376 * q^66 + 5272 * q^67 + 10416 * q^68 - 688 * q^69 + 12860 * q^70 - 2344 * q^71 + 4448 * q^72 - 4980 * q^73 + 2852 * q^74 + 7407 * q^75 + 15760 * q^76 + 3528 * q^77 + 16560 * q^78 + 10220 * q^79 + 7802 * q^80 + 14062 * q^81 + 17676 * q^82 + 12704 * q^83 + 19428 * q^84 + 4186 * q^85 + 3152 * q^86 + 11932 * q^87 + 20356 * q^88 + 8752 * q^89 + 6192 * q^90 + 10996 * q^91 + 15188 * q^92 + 3442 * q^93 + 3728 * q^94 + 5952 * q^95 - 13736 * q^96 - 5648 * q^97 - 808 * q^98 - 10558 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(165))\)

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
165.4.a	\(\chi_{165}(1, \cdot)\)	165.4.a.a	1	1
		165.4.a.b	1
		165.4.a.c	2
		165.4.a.d	3
		165.4.a.e	3
		165.4.a.f	3
		165.4.a.g	3
		165.4.a.h	4
165.4.c	\(\chi_{165}(34, \cdot)\)	165.4.c.a	14	1
		165.4.c.b	14
165.4.d	\(\chi_{165}(164, \cdot)\)	165.4.d.a	2	1
		165.4.d.b	2
		165.4.d.c	64
165.4.f	\(\chi_{165}(131, \cdot)\)	165.4.f.a	48	1
165.4.j	\(\chi_{165}(43, \cdot)\)	165.4.j.a	72	2
165.4.k	\(\chi_{165}(23, \cdot)\)	165.4.k.a	60	2
		165.4.k.b	60
165.4.m	\(\chi_{165}(16, \cdot)\)	165.4.m.a	24	4
		165.4.m.b	24
		165.4.m.c	24
		165.4.m.d	24
165.4.p	\(\chi_{165}(41, \cdot)\)	165.4.p.a	192	4
165.4.r	\(\chi_{165}(29, \cdot)\)	165.4.r.a	272	4
165.4.s	\(\chi_{165}(4, \cdot)\)	165.4.s.a	144	4
165.4.v	\(\chi_{165}(38, \cdot)\)	165.4.v.a	544	8
165.4.w	\(\chi_{165}(7, \cdot)\)	165.4.w.a	288	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(165))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(165)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 1}\)