Space of modular forms of level 184 and weight 4

• Label: 184.4
• Level: 184
• Weight: 4
• Dimension: 1732
• Nonzero newspaces: 6
• Newform subspaces: 15
• Sturm bound: 8448
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 15 \)
Sturm bound:			\(8448\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(184))\).

	Total	New	Old
Modular forms	3300	1816	1484
Cusp forms	3036	1732	1304
Eisenstein series	264	84	180

Trace form

1732 * q - 18 * q^2 - 14 * q^3 + 2 * q^4 + 4 * q^5 - 78 * q^6 - 38 * q^7 - 102 * q^8 - 18 * q^9 + 90 * q^10 + 66 * q^11 + 90 * q^12 - 44 * q^13 - 54 * q^14 - 262 * q^15 - 54 * q^16 - 88 * q^17 - 26 * q^18 - 110 * q^19 - 246 * q^20 + 192 * q^21 + 146 * q^22 + 338 * q^23 + 180 * q^24 + 146 * q^25 - 582 * q^26 - 326 * q^27 - 214 * q^28 - 396 * q^29 + 202 * q^30 - 598 * q^31 + 682 * q^32 - 732 * q^33 - 78 * q^34 - 1356 * q^35 - 46 * q^36 - 864 * q^37 + 370 * q^38 + 1406 * q^39 - 470 * q^40 + 1182 * q^41 + 426 * q^42 + 1590 * q^43 - 358 * q^44 + 2926 * q^45 - 326 * q^46 - 552 * q^47 - 1366 * q^48 + 2784 * q^49 + 30 * q^50 + 1038 * q^51 + 1098 * q^52 + 242 * q^53 - 1478 * q^54 - 1506 * q^55 + 618 * q^56 - 4304 * q^57 + 1658 * q^58 - 1700 * q^59 + 1322 * q^60 - 1100 * q^61 + 874 * q^62 + 474 * q^63 - 1174 * q^64 - 2196 * q^65 + 908 * q^66 - 398 * q^67 - 358 * q^68 - 224 * q^69 - 940 * q^70 - 1190 * q^71 + 58 * q^72 + 824 * q^73 + 2132 * q^74 + 10956 * q^75 + 15584 * q^76 + 2112 * q^77 + 18878 * q^78 + 7436 * q^79 + 10784 * q^80 + 6106 * q^81 - 434 * q^82 - 1748 * q^83 - 11698 * q^84 - 3034 * q^85 - 8794 * q^86 - 15856 * q^87 - 14598 * q^88 - 8146 * q^89 - 37336 * q^90 - 13068 * q^91 - 19864 * q^92 - 1280 * q^93 - 15508 * q^94 - 8706 * q^95 - 28804 * q^96 - 7090 * q^97 - 9762 * q^98 - 7920 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(184))\)

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
184.4.a	\(\chi_{184}(1, \cdot)\)	184.4.a.a	1	1
		184.4.a.b	1
		184.4.a.c	3
		184.4.a.d	3
		184.4.a.e	4
		184.4.a.f	4
184.4.b	\(\chi_{184}(93, \cdot)\)	184.4.b.a	30	1
		184.4.b.b	36
184.4.c	\(\chi_{184}(183, \cdot)\)	None	0	1
184.4.h	\(\chi_{184}(91, \cdot)\)	184.4.h.a	2	1
		184.4.h.b	4
		184.4.h.c	64
184.4.i	\(\chi_{184}(9, \cdot)\)	184.4.i.a	90	10
		184.4.i.b	90
184.4.j	\(\chi_{184}(11, \cdot)\)	184.4.j.a	700	10
184.4.o	\(\chi_{184}(7, \cdot)\)	None	0	10
184.4.p	\(\chi_{184}(13, \cdot)\)	184.4.p.a	700	10

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(184))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(184)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)