Space of modular forms of level 168 and weight 6

• Label: 168.6
• Level: 168
• Weight: 6
• Dimension: 1534
• Nonzero newspaces: 12
• Sturm bound: 9216
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(9216\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(168))\).

	Total	New	Old
Modular forms	3984	1574	2410
Cusp forms	3696	1534	2162
Eisenstein series	288	40	248

Trace form

1534 * q - 4 * q^2 + 16 * q^3 + 76 * q^4 - 196 * q^5 - 362 * q^6 + 160 * q^7 - 136 * q^8 + 556 * q^9 + 1388 * q^10 + 20 * q^11 + 970 * q^12 + 2232 * q^13 - 3692 * q^14 - 684 * q^15 - 5708 * q^16 - 1912 * q^17 - 434 * q^18 + 996 * q^19 + 17756 * q^20 + 4272 * q^21 + 19700 * q^22 - 1668 * q^23 - 722 * q^24 - 10182 * q^25 - 22900 * q^26 + 4540 * q^27 - 50396 * q^28 + 20844 * q^29 - 20190 * q^30 - 28228 * q^31 + 53236 * q^32 + 9878 * q^33 + 53220 * q^34 + 24108 * q^35 - 8960 * q^36 + 96 * q^37 - 73052 * q^38 + 3972 * q^39 + 9896 * q^40 + 51356 * q^41 + 44982 * q^42 - 68784 * q^43 + 15216 * q^44 + 7770 * q^45 - 30408 * q^46 + 58824 * q^47 - 22394 * q^48 - 78554 * q^49 - 67288 * q^50 + 83528 * q^51 + 78000 * q^52 + 50888 * q^53 + 132826 * q^54 + 48844 * q^55 + 238588 * q^56 - 57376 * q^57 + 2456 * q^58 - 290608 * q^59 - 315504 * q^60 - 157860 * q^61 - 360452 * q^62 + 214800 * q^63 - 784676 * q^64 + 59032 * q^65 - 28882 * q^66 + 370284 * q^67 + 207852 * q^68 + 110664 * q^69 + 634220 * q^70 + 324736 * q^71 + 159316 * q^72 + 210764 * q^73 + 429728 * q^74 - 316364 * q^75 + 423588 * q^76 - 209244 * q^77 - 247296 * q^78 - 940900 * q^79 - 774912 * q^80 + 117436 * q^81 - 522900 * q^82 - 52904 * q^83 + 284958 * q^84 + 157248 * q^85 - 807376 * q^86 + 10008 * q^87 - 648556 * q^88 - 536956 * q^89 + 485856 * q^90 + 237744 * q^91 + 1269276 * q^92 - 170262 * q^93 + 2047356 * q^94 + 268232 * q^95 + 343834 * q^96 + 1448552 * q^97 - 474304 * q^98 + 195704 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(168))\)

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
168.6.a	\(\chi_{168}(1, \cdot)\)	168.6.a.a	1	1
		168.6.a.b	1
		168.6.a.c	1
		168.6.a.d	1
		168.6.a.e	1
		168.6.a.f	1
		168.6.a.g	2
		168.6.a.h	2
		168.6.a.i	2
		168.6.a.j	2
168.6.b	\(\chi_{168}(55, \cdot)\)	None	0	1
168.6.c	\(\chi_{168}(85, \cdot)\)	168.6.c.a	28	1
		168.6.c.b	32
168.6.h	\(\chi_{168}(71, \cdot)\)	None	0	1
168.6.i	\(\chi_{168}(125, \cdot)\)	n/a	156	1
168.6.j	\(\chi_{168}(155, \cdot)\)	n/a	120	1
168.6.k	\(\chi_{168}(41, \cdot)\)	168.6.k.a	40	1
168.6.p	\(\chi_{168}(139, \cdot)\)	168.6.p.a	80	1
168.6.q	\(\chi_{168}(25, \cdot)\)	168.6.q.a	8	2
		168.6.q.b	10
		168.6.q.c	10
		168.6.q.d	12
168.6.t	\(\chi_{168}(19, \cdot)\)	n/a	160	2
168.6.u	\(\chi_{168}(17, \cdot)\)	168.6.u.a	80	2
168.6.v	\(\chi_{168}(11, \cdot)\)	n/a	312	2
168.6.ba	\(\chi_{168}(5, \cdot)\)	n/a	312	2
168.6.bb	\(\chi_{168}(23, \cdot)\)	None	0	2
168.6.bc	\(\chi_{168}(37, \cdot)\)	n/a	160	2
168.6.bd	\(\chi_{168}(31, \cdot)\)	None	0	2

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(168))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(168)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)