Space of modular forms of level 324 and weight 6

• Label: 324.6
• Level: 324
• Weight: 6
• Dimension: 6664
• Nonzero newspaces: 8
• Sturm bound: 34992
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(34992\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(324))\).

	Total	New	Old
Modular forms	14850	6776	8074
Cusp forms	14310	6664	7646
Eisenstein series	540	112	428

Trace form

6664 * q - 12 * q^2 - 20 * q^4 + 63 * q^5 - 18 * q^6 - 87 * q^7 - 9 * q^8 - 36 * q^9 + 35 * q^10 + 1257 * q^11 - 18 * q^12 - 691 * q^13 - 1527 * q^14 + 2488 * q^16 + 3450 * q^17 - 18 * q^18 + 522 * q^19 - 1251 * q^20 - 13779 * q^21 - 6576 * q^22 - 8403 * q^23 - 18 * q^24 + 17307 * q^25 - 27 * q^26 + 17523 * q^27 + 13191 * q^28 - 11679 * q^29 - 18 * q^30 - 17145 * q^31 - 7242 * q^32 - 36783 * q^33 - 19234 * q^34 - 11184 * q^35 - 18 * q^36 + 57842 * q^37 - 14886 * q^38 - 7945 * q^40 - 196917 * q^41 - 52173 * q^42 - 12447 * q^43 + 316071 * q^44 + 135990 * q^45 + 160839 * q^46 + 141921 * q^47 + 66411 * q^48 + 10195 * q^49 - 249432 * q^50 - 126315 * q^51 - 162655 * q^52 - 147594 * q^53 - 347148 * q^54 - 125730 * q^55 - 408483 * q^56 - 41562 * q^57 - 7441 * q^58 + 95097 * q^59 + 329805 * q^60 + 159173 * q^61 + 922869 * q^62 + 266274 * q^63 + 376009 * q^64 - 18297 * q^65 + 39222 * q^66 - 93789 * q^67 - 810006 * q^68 + 94914 * q^69 - 280071 * q^70 + 339060 * q^71 - 18 * q^72 + 149285 * q^73 - 20415 * q^74 - 56250 * q^75 - 107934 * q^76 - 563895 * q^77 + 2169 * q^78 + 54141 * q^79 - 455004 * q^81 + 45782 * q^82 - 263763 * q^83 - 2205 * q^84 + 193120 * q^85 + 279228 * q^86 + 405936 * q^87 + 319044 * q^88 - 445659 * q^89 + 856215 * q^90 + 141297 * q^91 - 106185 * q^92 + 1675710 * q^93 - 559731 * q^94 + 1074756 * q^95 - 1285965 * q^96 + 490337 * q^97 - 2615967 * q^98 - 908586 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(324))\)

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
324.6.a	\(\chi_{324}(1, \cdot)\)	324.6.a.a	3	1
		324.6.a.b	3
		324.6.a.c	4
		324.6.a.d	5
		324.6.a.e	5
324.6.b	\(\chi_{324}(323, \cdot)\)	n/a	116	1
324.6.e	\(\chi_{324}(109, \cdot)\)	324.6.e.a	2	2
		324.6.e.b	2
		324.6.e.c	2
		324.6.e.d	2
		324.6.e.e	4
		324.6.e.f	4
		324.6.e.g	4
		324.6.e.h	6
		324.6.e.i	6
		324.6.e.j	8
324.6.h	\(\chi_{324}(107, \cdot)\)	n/a	236	2
324.6.i	\(\chi_{324}(37, \cdot)\)	324.6.i.a	90	6
324.6.l	\(\chi_{324}(35, \cdot)\)	n/a	528	6
324.6.m	\(\chi_{324}(13, \cdot)\)	n/a	810	18
324.6.p	\(\chi_{324}(11, \cdot)\)	n/a	4824	18

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(324))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(324)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)