Space of modular forms of level 392 and weight 6

• Label: 392.6
• Level: 392
• Weight: 6
• Dimension: 12599
• Nonzero newspaces: 12
• Sturm bound: 56448
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(56448\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(392))\).

	Total	New	Old
Modular forms	23880	12793	11087
Cusp forms	23160	12599	10561
Eisenstein series	720	194	526

Trace form

12599 * q - 32 * q^2 - 10 * q^3 - 10 * q^4 - 74 * q^5 - 146 * q^6 - 36 * q^7 - 302 * q^8 - 1207 * q^9 + 602 * q^10 + 154 * q^11 + 1546 * q^12 + 2506 * q^13 - 36 * q^14 - 486 * q^15 - 3342 * q^16 - 4310 * q^17 + 1808 * q^18 - 11434 * q^19 + 9598 * q^20 + 6216 * q^21 + 26770 * q^22 + 13974 * q^23 - 8470 * q^24 - 8429 * q^25 - 30362 * q^26 - 36754 * q^27 - 33684 * q^28 - 3282 * q^29 - 18574 * q^30 + 14254 * q^31 + 50438 * q^32 + 14888 * q^33 + 98950 * q^34 + 2484 * q^35 + 43242 * q^36 + 3474 * q^37 - 66526 * q^38 + 15294 * q^39 - 21498 * q^40 + 67174 * q^41 + 46620 * q^42 - 73082 * q^43 - 102 * q^44 + 47290 * q^45 - 120890 * q^46 + 108126 * q^47 - 246534 * q^48 - 6294 * q^49 - 100094 * q^50 - 170234 * q^51 + 112558 * q^52 - 51542 * q^53 + 485714 * q^54 + 4302 * q^55 + 124662 * q^56 - 142428 * q^57 + 161206 * q^58 - 171290 * q^59 - 46554 * q^60 - 102146 * q^61 - 275386 * q^62 + 204888 * q^63 - 453154 * q^64 + 183944 * q^65 - 645438 * q^66 + 207026 * q^67 - 628086 * q^68 + 44648 * q^69 + 295956 * q^70 + 242858 * q^71 + 1142966 * q^72 + 213770 * q^73 + 1016194 * q^74 + 458230 * q^75 + 531194 * q^76 - 46386 * q^77 - 318430 * q^78 - 788594 * q^79 - 1020738 * q^80 - 1120899 * q^81 - 771874 * q^82 - 550726 * q^83 - 734976 * q^84 + 135608 * q^85 - 1132010 * q^86 + 1204686 * q^87 - 421982 * q^88 + 305782 * q^89 + 857774 * q^90 + 332868 * q^91 + 1652286 * q^92 - 526616 * q^93 + 2215914 * q^94 - 99746 * q^95 + 1119602 * q^96 + 490010 * q^97 - 93132 * q^98 - 2019596 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(392))\)

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
392.6.a	\(\chi_{392}(1, \cdot)\)	392.6.a.a	1	1
		392.6.a.b	1
		392.6.a.c	1
		392.6.a.d	2
		392.6.a.e	2
		392.6.a.f	2
		392.6.a.g	4
		392.6.a.h	4
		392.6.a.i	5
		392.6.a.j	5
		392.6.a.k	5
		392.6.a.l	5
		392.6.a.m	6
		392.6.a.n	8
392.6.b	\(\chi_{392}(197, \cdot)\)	n/a	200	1
392.6.e	\(\chi_{392}(195, \cdot)\)	n/a	196	1
392.6.f	\(\chi_{392}(391, \cdot)\)	None	0	1
392.6.i	\(\chi_{392}(177, \cdot)\)	392.6.i.a	2	2
		392.6.i.b	2
		392.6.i.c	2
		392.6.i.d	2
		392.6.i.e	2
		392.6.i.f	2
		392.6.i.g	4
		392.6.i.h	4
		392.6.i.i	4
		392.6.i.j	4
		392.6.i.k	4
		392.6.i.l	4
		392.6.i.m	8
		392.6.i.n	8
		392.6.i.o	10
		392.6.i.p	10
		392.6.i.q	12
		392.6.i.r	16
392.6.l	\(\chi_{392}(31, \cdot)\)	None	0	2
392.6.m	\(\chi_{392}(19, \cdot)\)	n/a	392	2
392.6.p	\(\chi_{392}(165, \cdot)\)	n/a	392	2
392.6.q	\(\chi_{392}(57, \cdot)\)	n/a	420	6
392.6.t	\(\chi_{392}(55, \cdot)\)	None	0	6
392.6.u	\(\chi_{392}(27, \cdot)\)	n/a	1668	6
392.6.x	\(\chi_{392}(29, \cdot)\)	n/a	1668	6
392.6.y	\(\chi_{392}(9, \cdot)\)	n/a	840	12
392.6.z	\(\chi_{392}(37, \cdot)\)	n/a	3336	12
392.6.bc	\(\chi_{392}(3, \cdot)\)	n/a	3336	12
392.6.bd	\(\chi_{392}(47, \cdot)\)	None	0	12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(392))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(392)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)