Space of modular forms of level 164 and weight 5

• Label: 164.5
• Level: 164
• Weight: 5
• Dimension: 1918
• Nonzero newspaces: 8
• Sturm bound: 8400
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(8400\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(164))\).

	Total	New	Old
Modular forms	3460	1994	1466
Cusp forms	3260	1918	1342
Eisenstein series	200	76	124

Trace form

1918 * q - 12 * q^2 - 52 * q^4 - 12 * q^5 - 20 * q^6 + 108 * q^8 - 202 * q^9 - 132 * q^10 - 20 * q^12 + 436 * q^13 - 20 * q^14 - 532 * q^16 - 684 * q^17 + 628 * q^18 + 428 * q^20 - 40 * q^21 - 20 * q^22 - 20 * q^24 + 818 * q^25 - 1924 * q^26 - 20 * q^28 - 204 * q^29 - 20 * q^30 + 3420 * q^31 + 2028 * q^32 - 7180 * q^33 + 2556 * q^34 - 9000 * q^35 - 2612 * q^36 - 16064 * q^37 - 20 * q^38 - 6160 * q^39 - 1832 * q^40 + 4618 * q^41 - 40 * q^42 + 4620 * q^43 - 20 * q^44 + 28228 * q^45 - 20 * q^46 + 18900 * q^47 - 20 * q^48 + 1278 * q^49 - 3452 * q^50 - 12540 * q^51 + 7596 * q^52 - 21384 * q^53 - 20 * q^54 - 20 * q^56 - 40 * q^57 + 636 * q^58 - 20 * q^60 + 13876 * q^61 - 20 * q^62 - 8212 * q^64 - 26864 * q^65 - 111620 * q^66 - 52080 * q^67 - 53224 * q^68 - 5800 * q^69 + 41780 * q^70 + 33600 * q^71 + 112408 * q^72 + 49556 * q^73 + 100436 * q^74 + 109440 * q^75 + 190480 * q^76 + 44120 * q^77 + 88180 * q^78 + 24640 * q^79 + 38948 * q^80 - 13202 * q^81 - 51292 * q^82 - 25920 * q^83 - 114500 * q^84 - 95744 * q^85 - 147020 * q^86 - 66240 * q^87 - 177820 * q^88 - 53484 * q^89 - 276392 * q^90 - 131200 * q^91 - 83180 * q^92 - 40360 * q^93 - 44480 * q^94 + 6720 * q^95 + 98980 * q^96 + 83156 * q^97 + 177288 * q^98 + 136080 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(164))\)

We only show spaces with odd 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
164.5.c	\(\chi_{164}(83, \cdot)\)	164.5.c.a	80	1
164.5.d	\(\chi_{164}(163, \cdot)\)	164.5.d.a	2	1
		164.5.d.b	2
		164.5.d.c	2
		164.5.d.d	2
		164.5.d.e	2
		164.5.d.f	72
164.5.e	\(\chi_{164}(91, \cdot)\)	n/a	164	2
164.5.h	\(\chi_{164}(85, \cdot)\)	164.5.h.a	56	4
164.5.j	\(\chi_{164}(51, \cdot)\)	n/a	328	4
164.5.l	\(\chi_{164}(23, \cdot)\)	n/a	328	4
164.5.n	\(\chi_{164}(39, \cdot)\)	n/a	656	8
164.5.p	\(\chi_{164}(13, \cdot)\)	n/a	224	16

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(164))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(164)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 2}\)