Space of modular forms of level 368 and weight 4

• Label: 368.4
• Level: 368
• Weight: 4
• Dimension: 7007
• Nonzero newspaces: 8
• Sturm bound: 33792
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(33792\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(368))\).

	Total	New	Old
Modular forms	12980	7195	5785
Cusp forms	12364	7007	5357
Eisenstein series	616	188	428

Trace form

7007 * q - 40 * q^2 - 37 * q^3 - 60 * q^4 - 47 * q^5 + 20 * q^6 + 15 * q^7 + 44 * q^8 + 11 * q^9 + 92 * q^10 - 157 * q^11 - 244 * q^12 - 95 * q^13 - 420 * q^14 + 231 * q^15 - 604 * q^16 - 191 * q^17 - 392 * q^18 + 107 * q^19 + 348 * q^20 + 33 * q^21 + 1132 * q^22 - 89 * q^23 + 1608 * q^24 + 231 * q^25 + 484 * q^26 - 97 * q^27 - 604 * q^28 - 47 * q^29 - 2516 * q^30 - 1089 * q^31 - 1980 * q^32 - 443 * q^33 - 916 * q^34 - 1081 * q^35 + 1148 * q^36 + 289 * q^37 + 2420 * q^38 - 209 * q^39 + 2628 * q^40 + 385 * q^41 + 1316 * q^42 + 1747 * q^43 - 1780 * q^44 - 498 * q^45 - 1176 * q^46 + 2878 * q^47 - 3580 * q^48 - 753 * q^49 - 1496 * q^50 + 2567 * q^51 + 428 * q^52 + 1185 * q^53 + 2708 * q^54 + 143 * q^55 + 932 * q^56 + 341 * q^57 - 60 * q^58 - 4781 * q^59 + 340 * q^60 - 2975 * q^61 + 116 * q^62 - 5817 * q^63 - 1068 * q^64 + 973 * q^65 + 812 * q^66 - 3541 * q^67 + 1716 * q^68 - 859 * q^69 - 408 * q^70 + 1423 * q^71 - 2228 * q^72 - 319 * q^73 + 860 * q^74 - 5103 * q^75 + 2412 * q^76 - 2643 * q^77 + 1500 * q^78 + 3197 * q^79 + 5252 * q^80 - 3785 * q^81 + 1364 * q^82 + 6817 * q^83 - 3964 * q^84 + 6637 * q^85 - 7572 * q^86 + 12441 * q^87 - 3100 * q^88 + 6041 * q^89 - 3836 * q^90 + 6382 * q^91 - 676 * q^92 + 14742 * q^93 + 6452 * q^94 - 3581 * q^95 + 8820 * q^96 + 6233 * q^97 - 672 * q^98 - 2051 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(368))\)

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
368.4.a	\(\chi_{368}(1, \cdot)\)	368.4.a.a	1	1
		368.4.a.b	1
		368.4.a.c	1
		368.4.a.d	1
		368.4.a.e	1
		368.4.a.f	2
		368.4.a.g	2
		368.4.a.h	3
		368.4.a.i	3
		368.4.a.j	3
		368.4.a.k	3
		368.4.a.l	4
		368.4.a.m	4
		368.4.a.n	4
368.4.b	\(\chi_{368}(185, \cdot)\)	None	0	1
368.4.c	\(\chi_{368}(367, \cdot)\)	368.4.c.a	12	1
		368.4.c.b	24
368.4.h	\(\chi_{368}(183, \cdot)\)	None	0	1
368.4.i	\(\chi_{368}(91, \cdot)\)	n/a	284	2
368.4.j	\(\chi_{368}(93, \cdot)\)	n/a	264	2
368.4.m	\(\chi_{368}(49, \cdot)\)	n/a	350	10
368.4.n	\(\chi_{368}(7, \cdot)\)	None	0	10
368.4.s	\(\chi_{368}(15, \cdot)\)	n/a	360	10
368.4.t	\(\chi_{368}(9, \cdot)\)	None	0	10
368.4.w	\(\chi_{368}(13, \cdot)\)	n/a	2840	20
368.4.x	\(\chi_{368}(11, \cdot)\)	n/a	2840	20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(368))\) into lower level spaces

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