Space of modular forms of level 368 and weight 2

• Label: 368.2
• Level: 368
• Weight: 2
• Dimension: 2273
• Nonzero newspaces: 8
• Newform subspaces: 28
• Sturm bound: 16896
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(16896\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(368))\).

	Total	New	Old
Modular forms	4532	2461	2071
Cusp forms	3917	2273	1644
Eisenstein series	615	188	427

Trace form

2273 * q - 40 * q^2 - 29 * q^3 - 44 * q^4 - 51 * q^5 - 52 * q^6 - 33 * q^7 - 52 * q^8 - 11 * q^9 - 44 * q^10 - 37 * q^11 - 36 * q^12 - 51 * q^13 - 36 * q^14 - 41 * q^15 - 28 * q^16 - 91 * q^17 - 48 * q^18 - 45 * q^19 - 52 * q^20 - 63 * q^21 - 44 * q^22 - 33 * q^23 - 88 * q^24 - 11 * q^25 - 52 * q^26 - 17 * q^27 - 60 * q^28 - 67 * q^29 - 36 * q^30 - q^31 - 60 * q^32 - 91 * q^33 - 52 * q^34 - 25 * q^35 - 36 * q^36 - 67 * q^37 - 20 * q^38 - 33 * q^39 - 28 * q^40 - 11 * q^41 - 44 * q^42 - 53 * q^43 - 36 * q^44 - 70 * q^45 - 56 * q^46 - 98 * q^47 - 60 * q^48 - 111 * q^49 - 32 * q^50 - 41 * q^51 - 36 * q^52 - 35 * q^53 - 44 * q^54 - 33 * q^55 - 28 * q^56 - 11 * q^57 - 20 * q^58 - 21 * q^59 - 44 * q^60 - 19 * q^61 - 76 * q^62 - 41 * q^63 - 44 * q^64 - 107 * q^65 - 52 * q^66 - 13 * q^67 - 44 * q^68 - 43 * q^69 - 104 * q^70 - 33 * q^71 - 52 * q^72 - 11 * q^73 - 44 * q^74 - 111 * q^75 - 68 * q^76 - 107 * q^77 - 36 * q^78 - 99 * q^79 - 60 * q^80 - 295 * q^81 - 44 * q^82 - 95 * q^83 - 28 * q^84 - 195 * q^85 - 44 * q^86 - 231 * q^87 - 60 * q^88 - 99 * q^89 - 36 * q^90 - 162 * q^91 - 20 * q^92 - 274 * q^93 - 12 * q^94 - 141 * q^95 - 12 * q^96 - 179 * q^97 - 32 * q^98 - 227 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)

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
368.2.a	\(\chi_{368}(1, \cdot)\)	368.2.a.a	1	1
		368.2.a.b	1
		368.2.a.c	1
		368.2.a.d	1
		368.2.a.e	1
		368.2.a.f	1
		368.2.a.g	1
		368.2.a.h	2
		368.2.a.i	2
368.2.b	\(\chi_{368}(185, \cdot)\)	None	0	1
368.2.c	\(\chi_{368}(367, \cdot)\)	368.2.c.a	4	1
		368.2.c.b	8
368.2.h	\(\chi_{368}(183, \cdot)\)	None	0	1
368.2.i	\(\chi_{368}(91, \cdot)\)	368.2.i.a	12	2
		368.2.i.b	80
368.2.j	\(\chi_{368}(93, \cdot)\)	368.2.j.a	2	2
		368.2.j.b	4
		368.2.j.c	12
		368.2.j.d	24
		368.2.j.e	46
368.2.m	\(\chi_{368}(49, \cdot)\)	368.2.m.a	10	10
		368.2.m.b	10
		368.2.m.c	10
		368.2.m.d	20
		368.2.m.e	30
		368.2.m.f	30
368.2.n	\(\chi_{368}(7, \cdot)\)	None	0	10
368.2.s	\(\chi_{368}(15, \cdot)\)	368.2.s.a	40	10
		368.2.s.b	80
368.2.t	\(\chi_{368}(9, \cdot)\)	None	0	10
368.2.w	\(\chi_{368}(13, \cdot)\)	368.2.w.a	920	20
368.2.x	\(\chi_{368}(11, \cdot)\)	368.2.x.a	920	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(368))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(368)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 1}\)