Space of modular forms of level 75 and weight 14

• Label: 75.14
• Level: 75
• Weight: 14
• Dimension: 1777
• Nonzero newspaces: 6
• Sturm bound: 5600
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(5600\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(75))\).

	Total	New	Old
Modular forms	2656	1817	839
Cusp forms	2544	1777	767
Eisenstein series	112	40	72

Trace form

1777 * q + 190 * q^2 + 3119 * q^3 - 36704 * q^4 + 80394 * q^5 - 1596 * q^6 - 457956 * q^7 + 5622672 * q^8 - 531451 * q^9 + 13131776 * q^10 + 9331852 * q^11 - 72303790 * q^12 - 100724786 * q^13 + 359155680 * q^14 - 120036334 * q^15 + 628129484 * q^16 + 1127481122 * q^17 + 341250740 * q^18 - 1582557304 * q^19 + 3729768156 * q^20 + 2496281394 * q^21 - 4203821756 * q^22 - 1571409088 * q^23 + 5261099688 * q^24 + 6130475654 * q^25 + 9776006052 * q^26 - 5123525761 * q^27 - 1821598692 * q^28 + 36780960082 * q^29 + 157234514 * q^30 + 28361297724 * q^31 + 20439372664 * q^32 - 23922574978 * q^33 - 57274846328 * q^34 - 77756433460 * q^35 - 139098779806 * q^36 + 239971054944 * q^37 - 65031693956 * q^38 + 100738333788 * q^39 - 536755840168 * q^40 + 84749369422 * q^41 + 508775245122 * q^42 + 640892044728 * q^43 + 160961186076 * q^44 - 481423190456 * q^45 - 939734276796 * q^46 - 111091979104 * q^47 + 634739033152 * q^48 + 1503775253057 * q^49 + 1094321303876 * q^50 + 493786818434 * q^51 - 1899261472248 * q^52 - 1501118875028 * q^53 - 894317026686 * q^54 + 1771540349284 * q^55 - 940033107720 * q^56 + 637902517234 * q^57 + 1286455344548 * q^58 - 987979483396 * q^59 + 185820458474 * q^60 - 3255871148906 * q^61 + 1534725885308 * q^62 - 2151300914516 * q^63 + 1246776544728 * q^64 + 6091679536222 * q^65 + 2048461129206 * q^66 + 955293818352 * q^67 + 4364083134680 * q^68 + 3848368012600 * q^69 - 8625465092060 * q^70 - 11911236986248 * q^71 - 6486841167018 * q^72 + 10832957582002 * q^73 + 24990431688260 * q^74 - 1996440253554 * q^75 - 4728074790216 * q^76 - 13038017630592 * q^77 - 18987003406712 * q^78 - 27584043974700 * q^79 + 6527614076596 * q^80 + 3447450569237 * q^81 + 3896769818888 * q^82 + 22105591900660 * q^83 - 18458927121370 * q^84 - 9138048361162 * q^85 - 19021585579088 * q^86 - 37082456288982 * q^87 + 14450238674092 * q^88 + 38601044851716 * q^89 + 8782014914606 * q^90 + 80736800513564 * q^91 + 29524033743304 * q^92 - 123339034103924 * q^93 - 312781591991012 * q^94 - 118465727353544 * q^95 + 98023901615826 * q^96 + 141997941280722 * q^97 + 174333692965846 * q^98 - 7959432246516 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(75))\)

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
75.14.a	\(\chi_{75}(1, \cdot)\)	75.14.a.a	1	1
		75.14.a.b	1
		75.14.a.c	2
		75.14.a.d	2
		75.14.a.e	2
		75.14.a.f	3
		75.14.a.g	4
		75.14.a.h	4
		75.14.a.i	5
		75.14.a.j	5
		75.14.a.k	6
		75.14.a.l	6
75.14.b	\(\chi_{75}(49, \cdot)\)	75.14.b.a	2	1
		75.14.b.b	2
		75.14.b.c	4
		75.14.b.d	4
		75.14.b.e	4
		75.14.b.f	6
		75.14.b.g	8
		75.14.b.h	10
75.14.e	\(\chi_{75}(32, \cdot)\)	n/a	152	2
75.14.g	\(\chi_{75}(16, \cdot)\)	n/a	264	4
75.14.i	\(\chi_{75}(4, \cdot)\)	n/a	256	4
75.14.l	\(\chi_{75}(2, \cdot)\)	n/a	1024	8

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)