Space of modular forms of level 3645 and weight 2

• Label: 3645.2
• Level: 3645
• Weight: 2
• Dimension: 340200
• Nonzero newspaces: 18
• Sturm bound: 1889568
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 3645 = 3^{6} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(1889568\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3645))\).

	Total	New	Old
Modular forms	477576	344088	133488
Cusp forms	467209	340200	127009
Eisenstein series	10367	3888	6479

Trace form

340200 * q - 216 * q^2 - 324 * q^3 - 360 * q^4 - 324 * q^5 - 972 * q^6 - 360 * q^7 - 216 * q^8 - 324 * q^9 - 756 * q^10 - 648 * q^11 - 324 * q^12 - 360 * q^13 - 216 * q^14 - 486 * q^15 - 1080 * q^16 - 216 * q^17 - 324 * q^18 - 504 * q^19 - 324 * q^20 - 972 * q^21 - 360 * q^22 - 216 * q^23 - 324 * q^24 - 540 * q^25 - 648 * q^26 - 324 * q^27 - 648 * q^28 - 216 * q^29 - 486 * q^30 - 1080 * q^31 - 216 * q^32 - 324 * q^33 - 360 * q^34 - 324 * q^35 - 972 * q^36 - 504 * q^37 - 216 * q^38 - 324 * q^39 - 540 * q^40 - 648 * q^41 - 324 * q^42 - 360 * q^43 - 216 * q^44 - 486 * q^45 - 1512 * q^46 - 216 * q^47 - 324 * q^48 - 360 * q^49 - 324 * q^50 - 972 * q^51 - 288 * q^52 - 216 * q^53 - 324 * q^54 - 972 * q^55 - 648 * q^56 - 324 * q^57 - 360 * q^58 - 216 * q^59 - 486 * q^60 - 1080 * q^61 - 216 * q^62 - 324 * q^63 - 360 * q^64 - 270 * q^65 - 972 * q^66 - 252 * q^67 + 162 * q^68 - 324 * q^69 - 432 * q^70 - 432 * q^71 - 324 * q^72 - 342 * q^73 + 216 * q^74 - 486 * q^75 - 756 * q^76 + 216 * q^77 - 324 * q^78 - 144 * q^79 + 81 * q^80 - 972 * q^81 - 486 * q^82 - 324 * q^84 - 432 * q^85 - 216 * q^86 - 324 * q^87 - 36 * q^88 + 54 * q^89 - 486 * q^90 - 1350 * q^91 + 432 * q^92 - 324 * q^93 - 144 * q^94 - 216 * q^95 - 972 * q^96 - 252 * q^97 - 324 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3645))\)

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
3645.2.a	\(\chi_{3645}(1, \cdot)\)	3645.2.a.a	3	1
		3645.2.a.b	3
		3645.2.a.c	6
		3645.2.a.d	6
		3645.2.a.e	9
		3645.2.a.f	9
		3645.2.a.g	15
		3645.2.a.h	15
		3645.2.a.i	18
		3645.2.a.j	18
		3645.2.a.k	21
		3645.2.a.l	21
3645.2.b	\(\chi_{3645}(1459, \cdot)\)	n/a	204	1
3645.2.e	\(\chi_{3645}(1216, \cdot)\)	n/a	288	2
3645.2.f	\(\chi_{3645}(728, \cdot)\)	n/a	408	2
3645.2.j	\(\chi_{3645}(244, \cdot)\)	n/a	408	2
3645.2.k	\(\chi_{3645}(406, \cdot)\)	n/a	864	6
3645.2.m	\(\chi_{3645}(242, \cdot)\)	n/a	816	4
3645.2.p	\(\chi_{3645}(649, \cdot)\)	n/a	1260	6
3645.2.q	\(\chi_{3645}(136, \cdot)\)	n/a	2592	18
3645.2.r	\(\chi_{3645}(323, \cdot)\)	n/a	2520	12
3645.2.t	\(\chi_{3645}(109, \cdot)\)	n/a	3744	18
3645.2.w	\(\chi_{3645}(46, \cdot)\)	n/a	5832	54
3645.2.y	\(\chi_{3645}(53, \cdot)\)	n/a	7488	36
3645.2.ba	\(\chi_{3645}(19, \cdot)\)	n/a	8640	54
3645.2.bc	\(\chi_{3645}(16, \cdot)\)	n/a	52488	162
3645.2.be	\(\chi_{3645}(8, \cdot)\)	n/a	17280	108
3645.2.bh	\(\chi_{3645}(4, \cdot)\)	n/a	78408	162
3645.2.bj	\(\chi_{3645}(2, \cdot)\)	n/a	156816	324

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3645))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3645)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(729))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1215))\)\(^{\oplus 2}\)