Space of modular forms of level 343 and weight 4

• Label: 343.4
• Level: 343
• Weight: 4
• Dimension: 13608
• Nonzero newspaces: 6
• Sturm bound: 38416
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 343 = 7^{3} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(38416\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(343))\).

	Total	New	Old
Modular forms	14679	14040	639
Cusp forms	14133	13608	525
Eisenstein series	546	432	114

Trace form

13608 * q - 108 * q^2 - 114 * q^3 - 108 * q^4 - 96 * q^5 - 75 * q^6 - 126 * q^7 - 228 * q^8 - 150 * q^9 - 135 * q^10 - 108 * q^11 - 63 * q^12 - 105 * q^13 - 126 * q^14 - 129 * q^15 - 48 * q^16 - 30 * q^17 - 126 * q^18 - 264 * q^19 - 273 * q^20 - 126 * q^21 - 207 * q^22 + 102 * q^23 + 33 * q^24 + 102 * q^25 - 105 * q^26 - 75 * q^27 - 126 * q^28 - 189 * q^29 - 171 * q^30 - 240 * q^31 - 426 * q^32 - 54 * q^33 - 243 * q^34 - 126 * q^35 + 3678 * q^36 + 4134 * q^37 + 5115 * q^38 + 4053 * q^39 + 6351 * q^40 + 1449 * q^41 - 630 * q^42 - 1827 * q^43 - 7125 * q^44 - 8187 * q^45 - 10419 * q^46 - 4170 * q^47 - 15153 * q^48 - 4158 * q^49 - 8442 * q^50 - 7122 * q^51 - 11445 * q^52 - 2922 * q^53 - 4671 * q^54 - 1563 * q^55 + 882 * q^56 + 2727 * q^57 + 6945 * q^58 + 6018 * q^59 + 21483 * q^60 + 10404 * q^61 + 11727 * q^62 + 4410 * q^63 + 9750 * q^64 + 441 * q^65 - 51 * q^66 - 276 * q^67 - 567 * q^68 - 2427 * q^69 - 126 * q^70 - 1827 * q^71 + 78 * q^72 + 306 * q^73 - 297 * q^74 + 165 * q^75 + 273 * q^76 - 126 * q^77 + 7245 * q^78 + 438 * q^79 + 26997 * q^80 + 30555 * q^81 + 29043 * q^82 + 19761 * q^83 + 19509 * q^84 + 10287 * q^85 + 10305 * q^86 + 4077 * q^87 - 3579 * q^88 - 3246 * q^89 - 31839 * q^90 - 4746 * q^91 - 18957 * q^92 - 39966 * q^93 - 33609 * q^94 - 32784 * q^95 - 68397 * q^96 - 17829 * q^97 - 28644 * q^98 - 32235 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(343))\)

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
343.4.a	\(\chi_{343}(1, \cdot)\)	343.4.a.a	3	1
		343.4.a.b	3
		343.4.a.c	12
		343.4.a.d	18
		343.4.a.e	18
		343.4.a.f	18
343.4.c	\(\chi_{343}(18, \cdot)\)	n/a	144	2
343.4.e	\(\chi_{343}(50, \cdot)\)	n/a	390	6
343.4.g	\(\chi_{343}(30, \cdot)\)	n/a	780	12
343.4.i	\(\chi_{343}(8, \cdot)\)	n/a	4074	42
343.4.k	\(\chi_{343}(2, \cdot)\)	n/a	8148	84

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(343))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(343)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)