Space of modular forms of level 338 and weight 6

• Label: 338.6
• Level: 338
• Weight: 6
• Dimension: 5845
• Nonzero newspaces: 8
• Sturm bound: 42588
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(42588\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(338))\).

	Total	New	Old
Modular forms	17973	5845	12128
Cusp forms	17517	5845	11672
Eisenstein series	456	0	456

Trace form

5845 * q - 1192 * q^7 + 384 * q^8 + 2592 * q^9 + 120 * q^10 - 2136 * q^11 - 1152 * q^12 - 3144 * q^13 - 1056 * q^14 + 4752 * q^15 + 2048 * q^16 + 1938 * q^17 + 9720 * q^18 + 10472 * q^19 - 3936 * q^20 - 264 * q^21 - 6456 * q^23 - 18750 * q^25 - 30312 * q^27 - 19072 * q^28 - 8190 * q^29 + 36672 * q^30 + 93104 * q^31 + 110040 * q^33 + 10560 * q^34 - 60720 * q^35 - 42240 * q^36 - 107230 * q^37 - 103968 * q^38 - 89076 * q^39 - 59166 * q^41 - 288 * q^42 + 116008 * q^43 + 72960 * q^44 + 308850 * q^45 + 125760 * q^46 + 185856 * q^47 + 27088 * q^49 - 147624 * q^50 - 634128 * q^51 - 45104 * q^52 + 33336 * q^53 + 236448 * q^54 + 241320 * q^55 + 84480 * q^56 + 340368 * q^57 + 86616 * q^58 + 112992 * q^59 - 46848 * q^60 + 33930 * q^61 - 224352 * q^62 - 811224 * q^63 - 24576 * q^64 - 94467 * q^65 - 343680 * q^66 - 144280 * q^67 - 9696 * q^68 + 280704 * q^69 + 98208 * q^70 + 271536 * q^71 + 218112 * q^72 + 16880 * q^73 + 22776 * q^74 - 48840 * q^75 + 167552 * q^76 + 85872 * q^77 + 214128 * q^78 + 323520 * q^79 - 62976 * q^80 - 551880 * q^81 + 280728 * q^82 + 303072 * q^83 + 40320 * q^84 + 90018 * q^85 - 169152 * q^86 + 55632 * q^87 + 113952 * q^89 - 972000 * q^90 - 253004 * q^91 - 354048 * q^92 - 401520 * q^93 - 549600 * q^94 - 1282128 * q^95 - 762568 * q^97 - 681984 * q^98 + 568872 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(338))\)

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
338.6.a	\(\chi_{338}(1, \cdot)\)	338.6.a.a	1	1
		338.6.a.b	1
		338.6.a.c	1
		338.6.a.d	1
		338.6.a.e	1
		338.6.a.f	2
		338.6.a.g	2
		338.6.a.h	3
		338.6.a.i	3
		338.6.a.j	4
		338.6.a.k	4
		338.6.a.l	6
		338.6.a.m	6
		338.6.a.n	6
		338.6.a.o	6
		338.6.a.p	9
		338.6.a.q	9
338.6.b	\(\chi_{338}(337, \cdot)\)	338.6.b.a	2	1
		338.6.b.b	4
		338.6.b.c	4
		338.6.b.d	6
		338.6.b.e	8
		338.6.b.f	12
		338.6.b.g	12
		338.6.b.h	18
338.6.c	\(\chi_{338}(191, \cdot)\)	n/a	126	2
338.6.e	\(\chi_{338}(23, \cdot)\)	n/a	128	2
338.6.g	\(\chi_{338}(27, \cdot)\)	n/a	900	12
338.6.h	\(\chi_{338}(25, \cdot)\)	n/a	888	12
338.6.i	\(\chi_{338}(3, \cdot)\)	n/a	1848	24
338.6.k	\(\chi_{338}(17, \cdot)\)	n/a	1824	24

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(338))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(338)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 1}\)