Space of modular forms of level 405 and weight 3

• Label: 405.3
• Level: 405
• Weight: 3
• Dimension: 8280
• Nonzero newspaces: 12
• Newform subspaces: 50
• Sturm bound: 34992
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 50 \)
Sturm bound:			\(34992\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(405))\).

	Total	New	Old
Modular forms	12096	8616	3480
Cusp forms	11232	8280	2952
Eisenstein series	864	336	528

Trace form

8280 * q - 24 * q^2 - 36 * q^3 - 48 * q^4 - 45 * q^5 - 108 * q^6 - 46 * q^7 - 30 * q^8 - 36 * q^9 - 83 * q^10 - 72 * q^11 - 36 * q^12 - 58 * q^13 - 42 * q^14 - 54 * q^15 - 56 * q^16 - 30 * q^17 + 108 * q^18 + 134 * q^19 + 399 * q^20 + 162 * q^21 + 232 * q^22 + 390 * q^23 + 180 * q^24 + 9 * q^25 - 42 * q^26 - 90 * q^27 - 338 * q^28 - 510 * q^29 - 270 * q^30 - 426 * q^31 - 1188 * q^32 - 414 * q^33 - 236 * q^34 - 201 * q^35 - 828 * q^36 - 166 * q^37 + 36 * q^38 - 36 * q^39 + 301 * q^40 + 972 * q^41 + 954 * q^42 + 596 * q^43 + 2574 * q^44 + 378 * q^45 + 1034 * q^46 + 1254 * q^47 + 954 * q^48 + 196 * q^49 - 27 * q^50 + 144 * q^51 - 322 * q^52 - 534 * q^53 - 288 * q^54 - 563 * q^55 - 2538 * q^56 - 468 * q^57 - 1278 * q^58 - 1896 * q^59 - 873 * q^60 - 1170 * q^61 - 3594 * q^62 - 1116 * q^63 - 1910 * q^64 - 1629 * q^65 - 3996 * q^66 - 184 * q^67 - 3996 * q^68 - 2196 * q^69 + 303 * q^70 - 726 * q^71 - 3492 * q^72 + 428 * q^73 + 162 * q^74 - 54 * q^75 + 1308 * q^76 + 678 * q^77 - 450 * q^78 + 890 * q^79 + 1572 * q^80 + 36 * q^81 + 580 * q^82 + 1074 * q^83 + 1818 * q^84 + 217 * q^85 + 1800 * q^86 + 1980 * q^87 - 144 * q^88 + 2736 * q^89 + 2457 * q^90 + 1360 * q^91 + 7134 * q^92 + 4356 * q^93 - 146 * q^94 + 2307 * q^95 + 6498 * q^96 + 80 * q^97 + 5370 * q^98 + 3060 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(405))\)

We only show spaces with odd 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
405.3.c	\(\chi_{405}(161, \cdot)\)	405.3.c.a	16	1
		405.3.c.b	16
405.3.d	\(\chi_{405}(404, \cdot)\)	405.3.d.a	20	1
		405.3.d.b	24
405.3.g	\(\chi_{405}(82, \cdot)\)	405.3.g.a	4	2
		405.3.g.b	4
		405.3.g.c	8
		405.3.g.d	8
		405.3.g.e	8
		405.3.g.f	16
		405.3.g.g	20
		405.3.g.h	20
405.3.h	\(\chi_{405}(134, \cdot)\)	405.3.h.a	2	2
		405.3.h.b	2
		405.3.h.c	4
		405.3.h.d	4
		405.3.h.e	4
		405.3.h.f	4
		405.3.h.g	4
		405.3.h.h	4
		405.3.h.i	8
		405.3.h.j	8
		405.3.h.k	48
405.3.i	\(\chi_{405}(26, \cdot)\)	405.3.i.a	4	2
		405.3.i.b	4
		405.3.i.c	8
		405.3.i.d	8
		405.3.i.e	8
		405.3.i.f	32
405.3.l	\(\chi_{405}(28, \cdot)\)	405.3.l.a	4	4
		405.3.l.b	4
		405.3.l.c	4
		405.3.l.d	4
		405.3.l.e	8
		405.3.l.f	8
		405.3.l.g	8
		405.3.l.h	8
		405.3.l.i	8
		405.3.l.j	16
		405.3.l.k	16
		405.3.l.l	16
		405.3.l.m	16
		405.3.l.n	32
		405.3.l.o	32
405.3.n	\(\chi_{405}(44, \cdot)\)	405.3.n.a	204	6
405.3.o	\(\chi_{405}(71, \cdot)\)	405.3.o.a	144	6
405.3.s	\(\chi_{405}(37, \cdot)\)	405.3.s.a	408	12
405.3.u	\(\chi_{405}(11, \cdot)\)	405.3.u.a	1296	18
405.3.v	\(\chi_{405}(14, \cdot)\)	405.3.v.a	1908	18
405.3.w	\(\chi_{405}(7, \cdot)\)	405.3.w.a	3816	36

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(405))\) into lower level spaces

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