Space of modular forms of level 405 and weight 5

• Label: 405.5
• Level: 405
• Weight: 5
• Dimension: 16728
• Nonzero newspaces: 12
• Sturm bound: 58320
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(58320\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(405))\).

	Total	New	Old
Modular forms	23760	17064	6696
Cusp forms	22896	16728	6168
Eisenstein series	864	336	528

Trace form

16728 * q - 24 * q^2 - 36 * q^3 - 72 * q^4 - 27 * q^5 - 108 * q^6 + 38 * q^7 - 30 * q^8 - 36 * q^9 - 311 * q^10 - 1044 * q^11 - 36 * q^12 + 410 * q^13 + 2262 * q^14 - 54 * q^15 + 1360 * q^16 - 30 * q^17 + 3996 * q^18 + 974 * q^19 - 3381 * q^20 - 4698 * q^21 - 7088 * q^22 - 11454 * q^23 - 9540 * q^24 - 417 * q^25 - 42 * q^26 + 2826 * q^27 + 12190 * q^28 + 17958 * q^29 + 9450 * q^30 + 12066 * q^31 + 41652 * q^32 + 6390 * q^33 + 7780 * q^34 - 1821 * q^35 - 20268 * q^36 - 19606 * q^37 - 45108 * q^38 - 36 * q^39 - 16283 * q^40 + 27720 * q^41 + 36594 * q^42 - 424 * q^43 - 18162 * q^44 - 11286 * q^45 - 31702 * q^46 - 40614 * q^47 - 70326 * q^48 - 19568 * q^49 - 31959 * q^50 - 24804 * q^51 + 710 * q^52 + 13506 * q^53 + 26928 * q^54 + 16873 * q^55 + 128358 * q^56 + 42300 * q^57 + 41778 * q^58 + 92244 * q^59 + 58095 * q^60 + 48954 * q^61 + 153222 * q^62 + 28044 * q^63 + 22042 * q^64 - 36675 * q^65 - 198396 * q^66 - 4540 * q^67 - 228348 * q^68 - 41076 * q^69 - 35745 * q^70 + 39450 * q^71 + 276444 * q^72 + 8312 * q^73 + 140850 * q^74 - 54 * q^75 - 95292 * q^76 + 45930 * q^77 + 88974 * q^78 - 56842 * q^79 - 128028 * q^80 - 23292 * q^81 - 92828 * q^82 - 123810 * q^83 - 307926 * q^84 + 8209 * q^85 - 147744 * q^86 - 252036 * q^87 + 240984 * q^88 + 205236 * q^89 + 1485 * q^90 + 158500 * q^91 + 169926 * q^92 - 6660 * q^93 + 51070 * q^94 + 23871 * q^95 + 75186 * q^96 - 163276 * q^97 - 306102 * q^98 - 8604 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(405))\)

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
405.5.c	\(\chi_{405}(161, \cdot)\)	405.5.c.a	32	1
		405.5.c.b	32
405.5.d	\(\chi_{405}(404, \cdot)\)	405.5.d.a	44	1
		405.5.d.b	48
405.5.g	\(\chi_{405}(82, \cdot)\)	n/a	184	2
405.5.h	\(\chi_{405}(134, \cdot)\)	n/a	188	2
405.5.i	\(\chi_{405}(26, \cdot)\)	n/a	128	2
405.5.l	\(\chi_{405}(28, \cdot)\)	n/a	376	4
405.5.n	\(\chi_{405}(44, \cdot)\)	n/a	420	6
405.5.o	\(\chi_{405}(71, \cdot)\)	n/a	288	6
405.5.s	\(\chi_{405}(37, \cdot)\)	n/a	840	12
405.5.u	\(\chi_{405}(11, \cdot)\)	n/a	2592	18
405.5.v	\(\chi_{405}(14, \cdot)\)	n/a	3852	18
405.5.w	\(\chi_{405}(7, \cdot)\)	n/a	7704	36

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(405))\) into lower level spaces

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