Space of modular forms of level 126 and weight 14

• Label: 126.14
• Level: 126
• Weight: 14
• Dimension: 1420
• Nonzero newspaces: 10
• Sturm bound: 12096
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(12096\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(126))\).

	Total	New	Old
Modular forms	5712	1420	4292
Cusp forms	5520	1420	4100
Eisenstein series	192	0	192

Trace form

1420 * q + 256 * q^2 - 2658 * q^3 + 73728 * q^4 + 54330 * q^5 - 120192 * q^6 - 942750 * q^7 - 524288 * q^8 + 5473650 * q^9 - 9919872 * q^10 + 11475870 * q^11 - 7667712 * q^12 - 28657094 * q^13 - 151087616 * q^14 + 540874632 * q^15 + 167772160 * q^16 - 428492712 * q^17 + 1256932608 * q^18 - 1712239598 * q^19 - 544137216 * q^20 - 1400275986 * q^21 + 2750822784 * q^22 - 107918268 * q^23 - 492306432 * q^24 - 8767774766 * q^25 - 3653129344 * q^26 + 11185324956 * q^27 + 941572096 * q^28 + 3525256968 * q^29 - 1765818624 * q^30 - 58609465316 * q^31 + 4294967296 * q^32 + 100741084194 * q^33 + 17232277632 * q^34 - 135864706998 * q^35 - 18681225216 * q^36 + 15990875700 * q^37 + 80677736192 * q^38 + 61373778300 * q^39 - 40631795712 * q^40 - 405641924346 * q^41 + 3100930560 * q^42 + 218023618578 * q^43 + 98021769216 * q^44 + 432194132544 * q^45 - 290650513152 * q^46 - 1244811034248 * q^47 + 76000788480 * q^48 + 391268659786 * q^49 + 1212942905344 * q^50 + 584346425850 * q^51 + 7435214848 * q^52 - 2345928725820 * q^53 + 652001304960 * q^54 + 967686327936 * q^55 + 317467918336 * q^56 + 651762927810 * q^57 + 9823577088 * q^58 - 4006797968760 * q^59 - 1157736923136 * q^60 - 555956346602 * q^61 + 4387482482432 * q^62 + 6519757964580 * q^63 - 2473901162496 * q^64 - 9574777536120 * q^65 - 6246514827264 * q^66 + 598700435894 * q^67 + 1933242703872 * q^68 + 12214964515644 * q^69 - 4106451606144 * q^70 - 5940783443688 * q^71 - 4460656459776 * q^72 - 3198536795588 * q^73 - 6461151432448 * q^74 - 1098871451670 * q^75 + 2868672200704 * q^76 + 31824994842738 * q^77 - 7243221257472 * q^78 - 8300363139100 * q^79 - 6437719769088 * q^80 - 21547298279874 * q^81 + 9559658231040 * q^82 + 40187511290454 * q^83 + 3184082313216 * q^84 + 3773895865764 * q^85 + 6209700599936 * q^86 + 17549651866212 * q^87 - 20279534813184 * q^88 - 88331699432880 * q^89 - 22781091680256 * q^90 + 47228903409454 * q^91 + 1673491365888 * q^92 + 131950757599380 * q^93 - 25331927633664 * q^94 - 46097434722144 * q^95 - 10063108374528 * q^96 - 42875205127538 * q^97 + 44280688671616 * q^98 - 87264950534940 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(126))\)

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
126.14.a	\(\chi_{126}(1, \cdot)\)	126.14.a.a	1	1
		126.14.a.b	1
		126.14.a.c	1
		126.14.a.d	1
		126.14.a.e	1
		126.14.a.f	1
		126.14.a.g	2
		126.14.a.h	2
		126.14.a.i	2
		126.14.a.j	2
		126.14.a.k	2
		126.14.a.l	2
		126.14.a.m	2
		126.14.a.n	3
		126.14.a.o	3
		126.14.a.p	3
		126.14.a.q	3
126.14.d	\(\chi_{126}(125, \cdot)\)	126.14.d.a	32	1
126.14.e	\(\chi_{126}(25, \cdot)\)	n/a	208	2
126.14.f	\(\chi_{126}(43, \cdot)\)	n/a	156	2
126.14.g	\(\chi_{126}(37, \cdot)\)	126.14.g.a	8	2
		126.14.g.b	8
		126.14.g.c	8
		126.14.g.d	8
		126.14.g.e	10
		126.14.g.f	10
		126.14.g.g	18
		126.14.g.h	18
126.14.h	\(\chi_{126}(67, \cdot)\)	n/a	208	2
126.14.k	\(\chi_{126}(17, \cdot)\)	126.14.k.a	72	2
126.14.l	\(\chi_{126}(5, \cdot)\)	n/a	208	2
126.14.m	\(\chi_{126}(41, \cdot)\)	n/a	208	2
126.14.t	\(\chi_{126}(47, \cdot)\)	n/a	208	2

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(126)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)