Space of modular forms of level 164 and weight 2

• Label: 164.2
• Level: 164
• Weight: 2
• Dimension: 450
• Nonzero newspaces: 8
• Newform subspaces: 10
• Sturm bound: 3360
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(3360\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(164))\).

	Total	New	Old
Modular forms	940	530	410
Cusp forms	741	450	291
Eisenstein series	199	80	119

Trace form

450 * q - 20 * q^2 - 20 * q^4 - 40 * q^5 - 20 * q^6 - 20 * q^8 - 40 * q^9 - 20 * q^10 - 20 * q^12 - 40 * q^13 - 20 * q^14 - 20 * q^16 - 40 * q^17 - 20 * q^18 - 20 * q^20 - 40 * q^21 - 20 * q^22 - 20 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^28 - 40 * q^29 - 20 * q^30 - 20 * q^31 - 20 * q^32 - 100 * q^33 - 20 * q^34 - 40 * q^35 - 20 * q^36 - 100 * q^37 - 20 * q^38 - 80 * q^39 - 60 * q^41 - 40 * q^42 - 20 * q^43 - 20 * q^44 - 120 * q^45 - 20 * q^46 - 60 * q^47 - 20 * q^48 - 80 * q^49 - 20 * q^50 - 60 * q^51 - 20 * q^52 - 60 * q^53 - 20 * q^54 - 20 * q^56 - 40 * q^57 - 20 * q^58 - 20 * q^60 - 40 * q^61 - 20 * q^62 - 20 * q^64 - 30 * q^65 + 60 * q^66 + 60 * q^67 + 80 * q^68 + 40 * q^69 + 180 * q^70 + 80 * q^71 + 160 * q^72 + 40 * q^73 + 100 * q^74 + 160 * q^75 + 280 * q^76 + 40 * q^77 + 180 * q^78 + 80 * q^79 + 180 * q^80 + 170 * q^81 + 220 * q^82 + 80 * q^83 + 220 * q^84 + 130 * q^85 + 180 * q^86 + 80 * q^87 + 180 * q^88 + 40 * q^89 + 280 * q^90 + 160 * q^91 + 100 * q^92 + 40 * q^93 + 160 * q^94 + 80 * q^95 + 180 * q^96 + 40 * q^97 + 80 * q^98 + 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)

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
164.2.a	\(\chi_{164}(1, \cdot)\)	164.2.a.a	4	1
164.2.b	\(\chi_{164}(81, \cdot)\)	164.2.b.a	4	1
164.2.f	\(\chi_{164}(9, \cdot)\)	164.2.f.a	6	2
164.2.g	\(\chi_{164}(37, \cdot)\)	164.2.g.a	16	4
164.2.i	\(\chi_{164}(3, \cdot)\)	164.2.i.a	4	4
		164.2.i.b	72
164.2.k	\(\chi_{164}(25, \cdot)\)	164.2.k.a	16	4
164.2.m	\(\chi_{164}(5, \cdot)\)	164.2.m.a	24	8
164.2.o	\(\chi_{164}(7, \cdot)\)	164.2.o.a	16	16
		164.2.o.b	288

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(164))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(164)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 2}\)