Space of modular forms of level 342 and weight 4

• Label: 342.4
• Level: 342
• Weight: 4
• Dimension: 2551
• Nonzero newspaces: 16
• Sturm bound: 25920
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(25920\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(342))\).

	Total	New	Old
Modular forms	10008	2551	7457
Cusp forms	9432	2551	6881
Eisenstein series	576	0	576

Trace form

2551 * q - 8 * q^2 - 6 * q^3 + 16 * q^4 - 24 * q^5 + 36 * q^6 + 8 * q^7 + 16 * q^8 + 210 * q^9 + 24 * q^10 - 54 * q^11 - 48 * q^12 + 260 * q^13 - 100 * q^14 - 180 * q^15 + 64 * q^16 - 384 * q^17 - 312 * q^18 - 986 * q^19 - 384 * q^20 + 72 * q^21 - 78 * q^22 + 900 * q^23 + 48 * q^24 + 1480 * q^25 + 1316 * q^26 + 752 * q^28 + 1386 * q^29 + 576 * q^30 + 278 * q^31 - 128 * q^32 - 1530 * q^33 - 684 * q^34 - 3972 * q^35 - 1032 * q^36 - 1558 * q^37 - 362 * q^38 + 1164 * q^39 + 96 * q^40 + 48 * q^41 + 1632 * q^42 - 2674 * q^43 - 1980 * q^44 - 6804 * q^45 - 6168 * q^46 - 3426 * q^47 + 3054 * q^49 + 2152 * q^50 + 4986 * q^51 + 536 * q^52 + 8844 * q^53 + 3492 * q^54 + 14328 * q^55 + 5504 * q^56 + 9093 * q^57 + 5448 * q^58 + 12834 * q^59 + 5040 * q^60 + 7946 * q^61 + 7892 * q^62 + 5604 * q^63 - 896 * q^64 - 4062 * q^65 - 5472 * q^66 - 11854 * q^67 - 3372 * q^68 - 13788 * q^69 - 14424 * q^70 - 23730 * q^71 - 3264 * q^72 - 5671 * q^73 - 2728 * q^74 - 6462 * q^75 + 340 * q^76 + 702 * q^77 - 264 * q^78 + 6614 * q^79 + 1344 * q^80 - 630 * q^81 + 8232 * q^82 + 1002 * q^83 - 1488 * q^84 + 1008 * q^85 - 412 * q^86 + 6408 * q^87 + 336 * q^88 + 6258 * q^89 + 864 * q^90 - 5744 * q^91 + 288 * q^92 + 5268 * q^93 - 8376 * q^94 - 27672 * q^95 - 768 * q^96 - 26290 * q^97 - 10764 * q^98 - 14526 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(342))\)

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
342.4.a	\(\chi_{342}(1, \cdot)\)	342.4.a.a	1	1
		342.4.a.b	1
		342.4.a.c	1
		342.4.a.d	1
		342.4.a.e	1
		342.4.a.f	2
		342.4.a.g	2
		342.4.a.h	2
		342.4.a.i	2
		342.4.a.j	2
		342.4.a.k	2
		342.4.a.l	3
		342.4.a.m	3
342.4.b	\(\chi_{342}(341, \cdot)\)	342.4.b.a	10	1
		342.4.b.b	10
342.4.e	\(\chi_{342}(115, \cdot)\)	n/a	108	2
342.4.f	\(\chi_{342}(7, \cdot)\)	n/a	120	2
342.4.g	\(\chi_{342}(163, \cdot)\)	342.4.g.a	2	2
		342.4.g.b	2
		342.4.g.c	2
		342.4.g.d	2
		342.4.g.e	4
		342.4.g.f	6
		342.4.g.g	6
		342.4.g.h	6
		342.4.g.i	10
		342.4.g.j	10
342.4.h	\(\chi_{342}(121, \cdot)\)	n/a	120	2
342.4.j	\(\chi_{342}(65, \cdot)\)	n/a	120	2
342.4.n	\(\chi_{342}(293, \cdot)\)	n/a	120	2
342.4.p	\(\chi_{342}(113, \cdot)\)	n/a	120	2
342.4.s	\(\chi_{342}(107, \cdot)\)	342.4.s.a	20	2
		342.4.s.b	20
342.4.u	\(\chi_{342}(55, \cdot)\)	n/a	150	6
342.4.v	\(\chi_{342}(25, \cdot)\)	n/a	360	6
342.4.w	\(\chi_{342}(43, \cdot)\)	n/a	360	6
342.4.x	\(\chi_{342}(29, \cdot)\)	n/a	360	6
342.4.bb	\(\chi_{342}(53, \cdot)\)	n/a	120	6
342.4.bf	\(\chi_{342}(155, \cdot)\)	n/a	360	6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(342)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)