Space of modular forms of level 182 and weight 2

• Label: 182.2
• Level: 182
• Weight: 2
• Dimension: 321
• Nonzero newspaces: 15
• Newform subspaces: 34
• Sturm bound: 4032
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 34 \)
Sturm bound:			\(4032\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(182))\).

	Total	New	Old
Modular forms	1152	321	831
Cusp forms	865	321	544
Eisenstein series	287	0	287

Trace form

321 * q + 3 * q^2 + 8 * q^3 - q^4 + 6 * q^5 - 5 * q^7 - 3 * q^8 - 21 * q^9 - 24 * q^10 - 12 * q^11 - 31 * q^13 - 9 * q^14 - 24 * q^15 - 9 * q^16 - 24 * q^17 - 15 * q^18 - 40 * q^19 - 20 * q^21 + 12 * q^22 + 11 * q^25 + 9 * q^26 - 40 * q^27 - 5 * q^28 - 36 * q^29 - 24 * q^30 - 40 * q^31 + 3 * q^32 - 72 * q^33 - 18 * q^34 - 66 * q^35 - 37 * q^36 - 28 * q^37 - 48 * q^38 - 60 * q^39 + 6 * q^40 - 72 * q^41 - 36 * q^42 - 60 * q^43 - 36 * q^44 - 72 * q^45 - 24 * q^46 - 24 * q^47 + 8 * q^48 - 33 * q^49 - 33 * q^50 - 48 * q^51 + 3 * q^52 - 30 * q^53 - 24 * q^54 - 48 * q^55 - 9 * q^56 - 40 * q^57 - 36 * q^58 - 24 * q^59 - 24 * q^60 - 32 * q^61 - 48 * q^62 - 113 * q^63 - 7 * q^64 - 96 * q^65 - 48 * q^66 - 76 * q^67 - 144 * q^69 - 30 * q^70 - 72 * q^71 - 33 * q^72 - 82 * q^73 + 36 * q^74 - 24 * q^75 + 56 * q^76 + 108 * q^77 + 84 * q^78 + 160 * q^79 + 207 * q^81 + 240 * q^82 + 120 * q^83 + 148 * q^84 + 294 * q^85 + 156 * q^86 + 288 * q^87 + 12 * q^88 + 198 * q^89 + 318 * q^90 + 253 * q^91 + 120 * q^92 + 200 * q^93 + 264 * q^94 + 264 * q^95 + 350 * q^97 + 99 * q^98 + 372 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)

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
182.2.a	\(\chi_{182}(1, \cdot)\)	182.2.a.a	1	1
		182.2.a.b	1
		182.2.a.c	1
		182.2.a.d	1
		182.2.a.e	1
182.2.d	\(\chi_{182}(155, \cdot)\)	182.2.d.a	2	1
		182.2.d.b	6
182.2.e	\(\chi_{182}(107, \cdot)\)	182.2.e.a	2	2
		182.2.e.b	2
		182.2.e.c	6
		182.2.e.d	10
182.2.f	\(\chi_{182}(53, \cdot)\)	182.2.f.a	2	2
		182.2.f.b	6
		182.2.f.c	8
182.2.g	\(\chi_{182}(29, \cdot)\)	182.2.g.a	2	2
		182.2.g.b	2
		182.2.g.c	2
		182.2.g.d	2
		182.2.g.e	4
182.2.h	\(\chi_{182}(9, \cdot)\)	182.2.h.a	2	2
		182.2.h.b	2
		182.2.h.c	6
		182.2.h.d	10
182.2.i	\(\chi_{182}(83, \cdot)\)	182.2.i.a	24	2
182.2.m	\(\chi_{182}(43, \cdot)\)	182.2.m.a	4	2
		182.2.m.b	12
182.2.n	\(\chi_{182}(25, \cdot)\)	182.2.n.a	4	2
		182.2.n.b	12
182.2.o	\(\chi_{182}(23, \cdot)\)	182.2.o.a	20	2
182.2.v	\(\chi_{182}(121, \cdot)\)	182.2.v.a	20	2
182.2.w	\(\chi_{182}(19, \cdot)\)	182.2.w.a	40	4
182.2.ba	\(\chi_{182}(41, \cdot)\)	182.2.ba.a	32	4
182.2.bb	\(\chi_{182}(5, \cdot)\)	182.2.bb.a	32	4
182.2.bc	\(\chi_{182}(45, \cdot)\)	182.2.bc.a	40	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(182))\) into lower level spaces

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