Space of modular forms of level 735 and weight 4

• Label: 735.4
• Level: 735
• Weight: 4
• Dimension: 36950
• Nonzero newspaces: 24
• Sturm bound: 150528
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(150528\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(735))\).

	Total	New	Old
Modular forms	57408	37534	19874
Cusp forms	55488	36950	18538
Eisenstein series	1920	584	1336

Trace form

36950 * q + 4 * q^2 - 12 * q^3 - 84 * q^4 - 42 * q^5 - 222 * q^6 - 168 * q^7 + 180 * q^8 + 120 * q^9 - 78 * q^10 - 56 * q^11 - 294 * q^12 - 208 * q^13 - 624 * q^14 - 291 * q^15 - 356 * q^16 - 8 * q^17 + 858 * q^18 + 1940 * q^19 + 1652 * q^20 + 1068 * q^21 + 1148 * q^22 - 960 * q^23 - 1266 * q^24 - 3532 * q^25 - 4592 * q^26 - 1332 * q^27 - 3048 * q^28 - 1420 * q^29 + 33 * q^30 - 412 * q^31 + 3308 * q^32 + 606 * q^33 + 4772 * q^34 + 2532 * q^35 + 6342 * q^36 - 984 * q^37 + 256 * q^38 + 1770 * q^39 - 2294 * q^40 - 1708 * q^41 + 4038 * q^42 + 4376 * q^43 + 12824 * q^44 + 429 * q^45 + 14828 * q^46 + 5272 * q^47 + 4536 * q^48 + 11376 * q^49 + 2116 * q^50 - 5742 * q^51 + 492 * q^52 - 3584 * q^53 - 16866 * q^54 - 14418 * q^55 - 13500 * q^56 - 10002 * q^57 - 24172 * q^58 - 19136 * q^59 - 8967 * q^60 - 8520 * q^61 - 9336 * q^62 + 2916 * q^63 + 22308 * q^64 + 15808 * q^65 + 21162 * q^66 + 27952 * q^67 + 29384 * q^68 + 6726 * q^69 + 21234 * q^70 + 10208 * q^71 - 9462 * q^72 + 1568 * q^73 + 11576 * q^74 - 2895 * q^75 - 10700 * q^76 + 1512 * q^77 - 7614 * q^78 - 11660 * q^79 - 36850 * q^80 - 12756 * q^81 - 67992 * q^82 - 41496 * q^83 - 34332 * q^84 - 29454 * q^85 - 34508 * q^86 + 4650 * q^87 - 23208 * q^88 + 516 * q^89 + 34896 * q^90 + 19884 * q^91 + 21636 * q^92 + 42906 * q^93 + 69656 * q^94 + 36568 * q^95 + 49464 * q^96 + 36156 * q^97 + 102108 * q^98 + 864 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(735))\)

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
735.4.a	\(\chi_{735}(1, \cdot)\)	735.4.a.a	1	1
		735.4.a.b	1
		735.4.a.c	1
		735.4.a.d	1
		735.4.a.e	1
		735.4.a.f	1
		735.4.a.g	1
		735.4.a.h	1
		735.4.a.i	1
		735.4.a.j	1
		735.4.a.k	2
		735.4.a.l	2
		735.4.a.m	2
		735.4.a.n	2
		735.4.a.o	2
		735.4.a.p	2
		735.4.a.q	2
		735.4.a.r	3
		735.4.a.s	3
		735.4.a.t	4
		735.4.a.u	4
		735.4.a.v	4
		735.4.a.w	4
		735.4.a.x	5
		735.4.a.y	5
		735.4.a.z	5
		735.4.a.ba	5
		735.4.a.bb	8
		735.4.a.bc	8
735.4.b	\(\chi_{735}(146, \cdot)\)	n/a	160	1
735.4.d	\(\chi_{735}(589, \cdot)\)	n/a	124	1
735.4.g	\(\chi_{735}(734, \cdot)\)	n/a	232	1
735.4.i	\(\chi_{735}(226, \cdot)\)	n/a	160	2
735.4.j	\(\chi_{735}(197, \cdot)\)	n/a	472	2
735.4.m	\(\chi_{735}(97, \cdot)\)	n/a	240	2
735.4.p	\(\chi_{735}(374, \cdot)\)	n/a	464	2
735.4.q	\(\chi_{735}(79, \cdot)\)	n/a	240	2
735.4.s	\(\chi_{735}(521, \cdot)\)	n/a	320	2
735.4.u	\(\chi_{735}(106, \cdot)\)	n/a	672	6
735.4.v	\(\chi_{735}(178, \cdot)\)	n/a	480	4
735.4.y	\(\chi_{735}(128, \cdot)\)	n/a	928	4
735.4.ba	\(\chi_{735}(104, \cdot)\)	n/a	1992	6
735.4.bd	\(\chi_{735}(64, \cdot)\)	n/a	1008	6
735.4.bf	\(\chi_{735}(41, \cdot)\)	n/a	1344	6
735.4.bg	\(\chi_{735}(16, \cdot)\)	n/a	1344	12
735.4.bi	\(\chi_{735}(13, \cdot)\)	n/a	2016	12
735.4.bj	\(\chi_{735}(8, \cdot)\)	n/a	3984	12
735.4.bm	\(\chi_{735}(26, \cdot)\)	n/a	2688	12
735.4.bo	\(\chi_{735}(4, \cdot)\)	n/a	2016	12
735.4.bp	\(\chi_{735}(59, \cdot)\)	n/a	3984	12
735.4.bt	\(\chi_{735}(2, \cdot)\)	n/a	7968	24
735.4.bu	\(\chi_{735}(52, \cdot)\)	n/a	4032	24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(735))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(735)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)