Space of modular forms of level 343 and weight 2

• Label: 343.2
• Level: 343
• Weight: 2
• Dimension: 4392
• Nonzero newspaces: 6
• Newform subspaces: 25
• Sturm bound: 19208
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 343 = 7^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(19208\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(343))\).

	Total	New	Old
Modular forms	5075	4824	251
Cusp forms	4530	4392	138
Eisenstein series	545	432	113

Trace form

4392 * q - 108 * q^2 - 109 * q^3 - 112 * q^4 - 111 * q^5 - 117 * q^6 - 126 * q^7 - 210 * q^8 - 118 * q^9 - 123 * q^10 - 117 * q^11 - 133 * q^12 - 119 * q^13 - 126 * q^14 - 219 * q^15 - 136 * q^16 - 123 * q^17 - 144 * q^18 - 125 * q^19 - 147 * q^20 - 126 * q^21 - 231 * q^22 - 129 * q^23 - 165 * q^24 - 136 * q^25 - 147 * q^26 - 145 * q^27 - 126 * q^28 - 225 * q^29 - 177 * q^30 - 137 * q^31 - 168 * q^32 - 153 * q^33 - 159 * q^34 - 126 * q^35 - 178 * q^36 - 87 * q^37 - 81 * q^38 - 63 * q^39 + 57 * q^40 - 63 * q^41 - 42 * q^42 - 155 * q^43 + 63 * q^44 + 27 * q^45 + 75 * q^46 - 69 * q^47 + 121 * q^48 - 42 * q^49 - 204 * q^50 - 9 * q^51 + 105 * q^52 - 75 * q^53 + 27 * q^54 + 33 * q^55 - 191 * q^57 - 27 * q^58 - 81 * q^59 - 21 * q^60 - 69 * q^61 - 117 * q^62 - 98 * q^63 - 178 * q^64 - 189 * q^65 - 249 * q^66 - 173 * q^67 - 231 * q^68 - 201 * q^69 - 126 * q^70 - 267 * q^71 - 300 * q^72 - 179 * q^73 - 219 * q^74 - 229 * q^75 - 245 * q^76 - 126 * q^77 - 147 * q^78 - 185 * q^79 - 165 * q^80 - 58 * q^81 - 21 * q^82 - 21 * q^83 + 105 * q^84 - 135 * q^85 + 57 * q^86 + 111 * q^87 + 177 * q^88 - 27 * q^89 + 459 * q^90 - 42 * q^91 - 69 * q^92 + 271 * q^93 + 129 * q^94 + 111 * q^95 + 441 * q^96 + 7 * q^97 + 168 * q^98 - 99 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(343))\)

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
343.2.a	\(\chi_{343}(1, \cdot)\)	343.2.a.a	3	1
		343.2.a.b	3
		343.2.a.c	6
		343.2.a.d	6
		343.2.a.e	6
343.2.c	\(\chi_{343}(18, \cdot)\)	343.2.c.a	6	2
		343.2.c.b	6
		343.2.c.c	12
		343.2.c.d	12
		343.2.c.e	12
343.2.e	\(\chi_{343}(50, \cdot)\)	343.2.e.a	6	6
		343.2.e.b	12
		343.2.e.c	48
		343.2.e.d	48
343.2.g	\(\chi_{343}(30, \cdot)\)	343.2.g.a	12	12
		343.2.g.b	12
		343.2.g.c	12
		343.2.g.d	12
		343.2.g.e	12
		343.2.g.f	12
		343.2.g.g	48
		343.2.g.h	48
		343.2.g.i	48
343.2.i	\(\chi_{343}(8, \cdot)\)	343.2.i.a	1302	42
343.2.k	\(\chi_{343}(2, \cdot)\)	343.2.k.a	2688	84

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(343))\) into lower level spaces

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