Space of modular forms of level 405 and weight 4

• Label: 405.4
• Level: 405
• Weight: 4
• Dimension: 12504
• Nonzero newspaces: 12
• Sturm bound: 46656
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(46656\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(405))\).

	Total	New	Old
Modular forms	17928	12840	5088
Cusp forms	17064	12504	4560
Eisenstein series	864	336	528

Trace form

12504 * q - 24 * q^2 - 36 * q^3 - 24 * q^4 - 24 * q^5 - 108 * q^6 - 76 * q^7 - 162 * q^8 - 36 * q^9 - 107 * q^10 + 54 * q^11 - 36 * q^12 + 68 * q^13 + 90 * q^14 - 54 * q^15 - 464 * q^16 - 426 * q^17 - 864 * q^18 - 958 * q^19 - 1203 * q^20 - 324 * q^21 + 316 * q^22 + 1548 * q^23 + 2124 * q^24 + 678 * q^25 + 6558 * q^26 + 1368 * q^27 + 2974 * q^28 + 2028 * q^29 + 702 * q^30 - 228 * q^31 - 2508 * q^32 - 900 * q^33 - 3392 * q^34 - 4185 * q^35 - 4716 * q^36 - 3406 * q^37 - 4824 * q^38 - 36 * q^39 - 341 * q^40 - 5694 * q^41 - 7146 * q^42 - 922 * q^43 - 4494 * q^44 - 1080 * q^45 + 2234 * q^46 + 5424 * q^47 + 4518 * q^48 + 4714 * q^49 + 10095 * q^50 + 5814 * q^51 + 7250 * q^52 + 9486 * q^53 + 13320 * q^54 + 2575 * q^55 + 17118 * q^56 + 4392 * q^57 + 3582 * q^58 + 5370 * q^59 + 1233 * q^60 - 48 * q^61 - 8010 * q^62 - 4032 * q^63 - 12038 * q^64 - 5526 * q^65 + 3780 * q^66 - 12946 * q^67 - 18096 * q^68 + 720 * q^69 - 7119 * q^70 - 4830 * q^71 - 3492 * q^72 - 3730 * q^73 - 16554 * q^74 - 54 * q^75 + 2436 * q^76 - 16584 * q^77 - 21834 * q^78 + 6296 * q^79 - 10482 * q^80 - 11628 * q^81 + 5788 * q^82 + 1908 * q^83 - 34794 * q^84 + 8317 * q^85 + 9420 * q^86 - 10980 * q^87 + 7848 * q^88 - 11742 * q^89 - 11151 * q^90 - 11294 * q^91 - 19566 * q^92 - 7632 * q^93 - 16802 * q^94 + 1005 * q^95 + 34362 * q^96 - 8014 * q^97 + 33438 * q^98 + 26388 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(405))\)

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
405.4.a	\(\chi_{405}(1, \cdot)\)	405.4.a.a	1	1
		405.4.a.b	1
		405.4.a.c	2
		405.4.a.d	2
		405.4.a.e	2
		405.4.a.f	2
		405.4.a.g	3
		405.4.a.h	3
		405.4.a.i	3
		405.4.a.j	3
		405.4.a.k	6
		405.4.a.l	6
		405.4.a.m	7
		405.4.a.n	7
405.4.b	\(\chi_{405}(244, \cdot)\)	405.4.b.a	4	1
		405.4.b.b	8
		405.4.b.c	8
		405.4.b.d	16
		405.4.b.e	16
		405.4.b.f	16
405.4.e	\(\chi_{405}(136, \cdot)\)	405.4.e.a	2	2
		405.4.e.b	2
		405.4.e.c	2
		405.4.e.d	2
		405.4.e.e	2
		405.4.e.f	2
		405.4.e.g	2
		405.4.e.h	2
		405.4.e.i	2
		405.4.e.j	2
		405.4.e.k	2
		405.4.e.l	2
		405.4.e.m	2
		405.4.e.n	2
		405.4.e.o	4
		405.4.e.p	4
		405.4.e.q	6
		405.4.e.r	6
		405.4.e.s	6
		405.4.e.t	6
		405.4.e.u	6
		405.4.e.v	6
		405.4.e.w	12
		405.4.e.x	12
405.4.f	\(\chi_{405}(242, \cdot)\)	n/a	136	2
405.4.j	\(\chi_{405}(109, \cdot)\)	n/a	140	2
405.4.k	\(\chi_{405}(46, \cdot)\)	n/a	216	6
405.4.m	\(\chi_{405}(53, \cdot)\)	n/a	280	4
405.4.p	\(\chi_{405}(19, \cdot)\)	n/a	312	6
405.4.q	\(\chi_{405}(16, \cdot)\)	n/a	1944	18
405.4.r	\(\chi_{405}(8, \cdot)\)	n/a	624	12
405.4.t	\(\chi_{405}(4, \cdot)\)	n/a	2880	18
405.4.x	\(\chi_{405}(2, \cdot)\)	n/a	5760	36

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(405))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(405)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)