Space of modular forms of level 182 and weight 4

• Label: 182.4
• Level: 182
• Weight: 4
• Dimension: 954
• Nonzero newspaces: 15
• Newform subspaces: 36
• Sturm bound: 8064
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 36 \)
Sturm bound:			\(8064\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(182))\).

	Total	New	Old
Modular forms	3168	954	2214
Cusp forms	2880	954	1926
Eisenstein series	288	0	288

Trace form

954 * q - 24 * q^3 + 48 * q^5 + 72 * q^6 + 24 * q^7 - 48 * q^8 - 84 * q^9 + 108 * q^10 + 156 * q^11 + 510 * q^13 - 144 * q^14 + 312 * q^15 - 174 * q^17 - 204 * q^18 - 1248 * q^19 - 24 * q^20 + 24 * q^21 + 432 * q^22 + 1044 * q^23 + 96 * q^24 + 330 * q^25 - 348 * q^26 + 504 * q^27 - 528 * q^28 - 3258 * q^29 - 1968 * q^30 - 1548 * q^31 + 228 * q^33 + 1680 * q^34 + 1620 * q^35 + 1872 * q^36 + 1290 * q^37 + 2520 * q^38 + 3060 * q^39 - 288 * q^40 + 4302 * q^41 + 288 * q^42 + 1368 * q^43 + 48 * q^44 - 54 * q^45 - 528 * q^46 - 1668 * q^47 + 192 * q^48 - 1656 * q^49 - 5436 * q^50 - 11148 * q^51 - 2016 * q^52 - 4692 * q^53 - 3024 * q^54 - 2664 * q^55 - 192 * q^56 + 504 * q^57 + 2196 * q^58 + 2856 * q^59 + 3120 * q^60 - 354 * q^61 + 3936 * q^62 + 816 * q^63 - 384 * q^64 + 1686 * q^65 + 6720 * q^66 + 6588 * q^67 + 1512 * q^68 + 10416 * q^69 + 2736 * q^70 + 6000 * q^71 + 1728 * q^72 + 9540 * q^73 + 4308 * q^74 + 19332 * q^75 + 3120 * q^76 + 12492 * q^77 - 3312 * q^78 + 2556 * q^79 - 288 * q^80 - 3912 * q^81 - 2940 * q^82 + 756 * q^83 - 4896 * q^84 - 17178 * q^85 - 8400 * q^86 - 28320 * q^87 - 2688 * q^88 - 28044 * q^89 - 26376 * q^90 - 26826 * q^91 - 7584 * q^92 - 30132 * q^93 - 17088 * q^94 - 20316 * q^95 + 384 * q^96 - 12360 * q^97 - 4224 * q^98 - 11400 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(182))\)

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
182.4.a	\(\chi_{182}(1, \cdot)\)	182.4.a.a	1	1
		182.4.a.b	1
		182.4.a.c	1
		182.4.a.d	1
		182.4.a.e	2
		182.4.a.f	2
		182.4.a.g	2
		182.4.a.h	2
		182.4.a.i	3
		182.4.a.j	3
182.4.d	\(\chi_{182}(155, \cdot)\)	182.4.d.a	2	1
		182.4.d.b	6
		182.4.d.c	12
182.4.e	\(\chi_{182}(107, \cdot)\)	182.4.e.a	28	2
		182.4.e.b	28
182.4.f	\(\chi_{182}(53, \cdot)\)	182.4.f.a	2	2
		182.4.f.b	6
		182.4.f.c	10
		182.4.f.d	14
		182.4.f.e	16
182.4.g	\(\chi_{182}(29, \cdot)\)	182.4.g.a	8	2
		182.4.g.b	10
		182.4.g.c	12
		182.4.g.d	14
182.4.h	\(\chi_{182}(9, \cdot)\)	182.4.h.a	28	2
		182.4.h.b	28
182.4.i	\(\chi_{182}(83, \cdot)\)	182.4.i.a	56	2
182.4.m	\(\chi_{182}(43, \cdot)\)	182.4.m.a	16	2
		182.4.m.b	24
182.4.n	\(\chi_{182}(25, \cdot)\)	182.4.n.a	56	2
182.4.o	\(\chi_{182}(23, \cdot)\)	182.4.o.a	56	2
182.4.v	\(\chi_{182}(121, \cdot)\)	182.4.v.a	56	2
182.4.w	\(\chi_{182}(19, \cdot)\)	182.4.w.a	112	4
182.4.ba	\(\chi_{182}(41, \cdot)\)	182.4.ba.a	112	4
182.4.bb	\(\chi_{182}(5, \cdot)\)	182.4.bb.a	112	4
182.4.bc	\(\chi_{182}(45, \cdot)\)	182.4.bc.a	112	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(182))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(182)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)