Space of modular forms of level 405 and weight 2

• Label: 405.2
• Level: 405
• Weight: 2
• Dimension: 4056
• Nonzero newspaces: 12
• Newform subspaces: 50
• Sturm bound: 23328
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 50 \)
Sturm bound:			\(23328\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(405))\).

	Total	New	Old
Modular forms	6264	4392	1872
Cusp forms	5401	4056	1345
Eisenstein series	863	336	527

Trace form

4056 * q - 24 * q^2 - 36 * q^3 - 36 * q^4 - 33 * q^5 - 108 * q^6 - 34 * q^7 - 36 * q^9 - 77 * q^10 - 54 * q^11 - 36 * q^12 - 22 * q^13 + 18 * q^14 - 54 * q^15 - 116 * q^16 + 6 * q^17 - 54 * q^18 - 70 * q^19 - 69 * q^20 - 162 * q^21 - 50 * q^22 - 90 * q^23 - 144 * q^24 - 75 * q^25 - 246 * q^26 - 90 * q^27 - 122 * q^28 - 78 * q^29 - 108 * q^30 - 138 * q^31 - 168 * q^32 - 90 * q^33 - 86 * q^34 - 81 * q^35 - 180 * q^36 - 58 * q^37 - 18 * q^38 - 36 * q^39 - 155 * q^40 - 114 * q^41 - 126 * q^42 - 82 * q^43 - 282 * q^44 - 108 * q^45 - 310 * q^46 - 210 * q^47 - 234 * q^48 - 128 * q^49 - 291 * q^50 - 234 * q^51 - 190 * q^52 - 234 * q^53 - 288 * q^54 - 155 * q^55 - 486 * q^56 - 144 * q^57 - 126 * q^58 - 174 * q^59 - 171 * q^60 - 150 * q^61 - 234 * q^62 - 144 * q^63 - 116 * q^64 - 45 * q^65 - 108 * q^66 - 58 * q^67 + 120 * q^68 + 72 * q^69 - 141 * q^70 + 138 * q^71 + 396 * q^72 - 4 * q^73 + 258 * q^74 - 54 * q^75 - 234 * q^76 + 210 * q^77 + 198 * q^78 - 106 * q^79 + 102 * q^80 + 36 * q^81 - 128 * q^82 + 90 * q^83 + 414 * q^84 - 161 * q^85 + 114 * q^86 + 252 * q^87 - 234 * q^88 - 24 * q^89 + 27 * q^90 - 260 * q^91 - 90 * q^92 - 72 * q^93 - 266 * q^94 - 219 * q^95 - 90 * q^96 - 214 * q^97 - 528 * q^98 - 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)

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
405.2.a	\(\chi_{405}(1, \cdot)\)	405.2.a.a	1	1
		405.2.a.b	1
		405.2.a.c	1
		405.2.a.d	1
		405.2.a.e	1
		405.2.a.f	1
		405.2.a.g	2
		405.2.a.h	2
		405.2.a.i	3
		405.2.a.j	3
405.2.b	\(\chi_{405}(244, \cdot)\)	405.2.b.a	4	1
		405.2.b.b	4
		405.2.b.c	4
		405.2.b.d	4
		405.2.b.e	4
405.2.e	\(\chi_{405}(136, \cdot)\)	405.2.e.a	2	2
		405.2.e.b	2
		405.2.e.c	2
		405.2.e.d	2
		405.2.e.e	2
		405.2.e.f	2
		405.2.e.g	2
		405.2.e.h	2
		405.2.e.i	4
		405.2.e.j	4
		405.2.e.k	4
		405.2.e.l	4
405.2.f	\(\chi_{405}(242, \cdot)\)	405.2.f.a	16	2
		405.2.f.b	24
405.2.j	\(\chi_{405}(109, \cdot)\)	405.2.j.a	4	2
		405.2.j.b	4
		405.2.j.c	4
		405.2.j.d	4
		405.2.j.e	4
		405.2.j.f	8
		405.2.j.g	8
		405.2.j.h	8
405.2.k	\(\chi_{405}(46, \cdot)\)	405.2.k.a	30	6
		405.2.k.b	42
405.2.m	\(\chi_{405}(53, \cdot)\)	405.2.m.a	8	4
		405.2.m.b	16
		405.2.m.c	16
		405.2.m.d	24
		405.2.m.e	24
405.2.p	\(\chi_{405}(19, \cdot)\)	405.2.p.a	96	6
405.2.q	\(\chi_{405}(16, \cdot)\)	405.2.q.a	306	18
		405.2.q.b	342
405.2.r	\(\chi_{405}(8, \cdot)\)	405.2.r.a	192	12
405.2.t	\(\chi_{405}(4, \cdot)\)	405.2.t.a	936	18
405.2.x	\(\chi_{405}(2, \cdot)\)	405.2.x.a	1872	36

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(405))\) into lower level spaces

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