Space of modular forms of level 294 and weight 4

• Label: 294.4
• Level: 294
• Weight: 4
• Dimension: 1693
• Nonzero newspaces: 8
• Sturm bound: 18816
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(18816\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(294))\).

	Total	New	Old
Modular forms	7296	1693	5603
Cusp forms	6816	1693	5123
Eisenstein series	480	0	480

Trace form

1693 * q - 2 * q^2 + 21 * q^3 + 4 * q^4 - 90 * q^5 - 66 * q^6 - 96 * q^7 - 8 * q^8 + 93 * q^9 + 132 * q^10 + 180 * q^11 + 84 * q^12 + 14 * q^13 - 522 * q^15 + 16 * q^16 - 150 * q^17 + 318 * q^18 + 788 * q^19 + 24 * q^20 + 648 * q^21 - 24 * q^22 + 120 * q^24 + 751 * q^25 + 836 * q^26 - 135 * q^27 + 96 * q^28 - 162 * q^29 - 1308 * q^30 - 1624 * q^31 - 32 * q^32 - 2664 * q^33 - 1380 * q^34 - 876 * q^35 - 1596 * q^36 - 7978 * q^37 - 4816 * q^38 - 2214 * q^39 - 1488 * q^40 - 534 * q^41 + 828 * q^42 + 2780 * q^43 + 3072 * q^44 + 7002 * q^45 + 9576 * q^46 + 8352 * q^47 + 432 * q^48 + 12228 * q^49 + 3490 * q^50 + 1134 * q^51 - 280 * q^52 + 2382 * q^53 - 306 * q^54 + 5688 * q^55 - 576 * q^56 + 1620 * q^57 - 2076 * q^58 - 6132 * q^59 - 576 * q^60 - 6346 * q^61 - 4648 * q^62 + 2406 * q^63 + 1600 * q^64 + 1572 * q^65 + 4104 * q^66 - 460 * q^67 - 600 * q^68 - 3816 * q^69 - 1008 * q^70 - 6840 * q^71 - 1416 * q^72 - 11590 * q^73 + 500 * q^74 - 9753 * q^75 - 784 * q^76 + 108 * q^77 - 6012 * q^78 - 4552 * q^79 - 1440 * q^80 - 14871 * q^81 - 4020 * q^82 - 13524 * q^83 - 912 * q^84 - 5820 * q^85 - 2248 * q^86 - 7098 * q^87 + 1248 * q^88 - 798 * q^89 - 2268 * q^90 + 8064 * q^91 - 3552 * q^92 + 15216 * q^93 - 3648 * q^94 + 21624 * q^95 + 480 * q^96 + 6674 * q^97 - 816 * q^98 + 16572 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(294))\)

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
294.4.a	\(\chi_{294}(1, \cdot)\)	294.4.a.a	1	1
		294.4.a.b	1
		294.4.a.c	1
		294.4.a.d	1
		294.4.a.e	1
		294.4.a.f	1
		294.4.a.g	1
		294.4.a.h	1
		294.4.a.i	1
		294.4.a.j	2
		294.4.a.k	2
		294.4.a.l	2
		294.4.a.m	2
		294.4.a.n	2
		294.4.a.o	2
294.4.d	\(\chi_{294}(293, \cdot)\)	294.4.d.a	16	1
		294.4.d.b	24
294.4.e	\(\chi_{294}(67, \cdot)\)	294.4.e.a	2	2
		294.4.e.b	2
		294.4.e.c	2
		294.4.e.d	2
		294.4.e.e	2
		294.4.e.f	2
		294.4.e.g	2
		294.4.e.h	2
		294.4.e.i	2
		294.4.e.j	2
		294.4.e.k	4
		294.4.e.l	4
		294.4.e.m	4
		294.4.e.n	4
		294.4.e.o	4
294.4.f	\(\chi_{294}(215, \cdot)\)	294.4.f.a	16	2
		294.4.f.b	16
		294.4.f.c	48
294.4.i	\(\chi_{294}(43, \cdot)\)	n/a	168	6
294.4.j	\(\chi_{294}(41, \cdot)\)	n/a	336	6
294.4.m	\(\chi_{294}(25, \cdot)\)	n/a	336	12
294.4.p	\(\chi_{294}(5, \cdot)\)	n/a	672	12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(294))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(294)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)