Space of modular forms of level 165 and weight 2

• Label: 165.2
• Level: 165
• Weight: 2
• Dimension: 599
• Nonzero newspaces: 12
• Newform subspaces: 25
• Sturm bound: 3840
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(3840\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(165))\).

	Total	New	Old
Modular forms	1120	703	417
Cusp forms	801	599	202
Eisenstein series	319	104	215

Trace form

599 * q + 5 * q^2 - 7 * q^3 - 11 * q^4 - q^5 - 39 * q^6 - 32 * q^7 - 31 * q^8 - 31 * q^9 - 55 * q^10 - 5 * q^11 - 55 * q^12 - 22 * q^13 - 36 * q^14 - 32 * q^15 - 147 * q^16 - 46 * q^17 - 35 * q^18 - 68 * q^19 - 41 * q^20 - 72 * q^21 - 111 * q^22 - 16 * q^23 - 39 * q^24 - 71 * q^25 - 62 * q^26 + 23 * q^27 - 64 * q^28 - 6 * q^29 - 19 * q^30 - 68 * q^31 + 33 * q^32 + 17 * q^33 - 62 * q^34 - 32 * q^35 - 31 * q^36 - 42 * q^37 - 32 * q^38 - 50 * q^39 + 29 * q^40 - 98 * q^41 - 16 * q^42 - 44 * q^43 + 13 * q^44 - 76 * q^45 - 88 * q^46 + 12 * q^47 + 29 * q^48 + 31 * q^49 + 55 * q^50 - 38 * q^51 + 134 * q^52 + 54 * q^53 + 21 * q^54 + 65 * q^55 + 200 * q^56 + 108 * q^57 + 206 * q^58 + 128 * q^59 + 125 * q^60 + 66 * q^61 + 136 * q^62 + 68 * q^63 + 213 * q^64 + 78 * q^65 + 97 * q^66 + 24 * q^67 + 90 * q^68 + 34 * q^69 - 76 * q^70 - 32 * q^71 + 9 * q^72 - 146 * q^73 - 86 * q^74 - 82 * q^75 - 292 * q^76 - 92 * q^77 - 74 * q^78 - 200 * q^79 - 177 * q^80 - 51 * q^81 - 94 * q^82 - 200 * q^83 - 4 * q^84 - 146 * q^85 - 140 * q^86 - 114 * q^87 - 163 * q^88 - 58 * q^89 + 105 * q^90 - 88 * q^91 + 28 * q^92 - 18 * q^93 + 120 * q^94 + 22 * q^95 + 173 * q^96 + 74 * q^97 + 157 * q^98 + 145 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)

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
165.2.a	\(\chi_{165}(1, \cdot)\)	165.2.a.a	2	1
		165.2.a.b	2
		165.2.a.c	3
165.2.c	\(\chi_{165}(34, \cdot)\)	165.2.c.a	6	1
		165.2.c.b	6
165.2.d	\(\chi_{165}(164, \cdot)\)	165.2.d.a	2	1
		165.2.d.b	2
		165.2.d.c	16
165.2.f	\(\chi_{165}(131, \cdot)\)	165.2.f.a	8	1
		165.2.f.b	8
165.2.j	\(\chi_{165}(43, \cdot)\)	165.2.j.a	24	2
165.2.k	\(\chi_{165}(23, \cdot)\)	165.2.k.a	4	2
		165.2.k.b	4
		165.2.k.c	16
		165.2.k.d	16
165.2.m	\(\chi_{165}(16, \cdot)\)	165.2.m.a	8	4
		165.2.m.b	8
		165.2.m.c	8
		165.2.m.d	8
165.2.p	\(\chi_{165}(41, \cdot)\)	165.2.p.a	16	4
		165.2.p.b	48
165.2.r	\(\chi_{165}(29, \cdot)\)	165.2.r.a	80	4
165.2.s	\(\chi_{165}(4, \cdot)\)	165.2.s.a	48	4
165.2.v	\(\chi_{165}(38, \cdot)\)	165.2.v.a	160	8
165.2.w	\(\chi_{165}(7, \cdot)\)	165.2.w.a	96	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(165))\) into lower level spaces

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