Space of modular forms of level 324 and weight 2

• Label: 324.2
• Level: 324
• Weight: 2
• Dimension: 1288
• Nonzero newspaces: 8
• Newform subspaces: 21
• Sturm bound: 11664
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(11664\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(324))\).

	Total	New	Old
Modular forms	3186	1400	1786
Cusp forms	2647	1288	1359
Eisenstein series	539	112	427

Trace form

1288 * q - 12 * q^2 - 20 * q^4 - 27 * q^5 - 18 * q^6 - 3 * q^7 - 9 * q^8 - 36 * q^9 - 25 * q^10 - 3 * q^11 - 18 * q^12 - 37 * q^13 + 3 * q^14 - 8 * q^16 - 6 * q^17 - 18 * q^18 + 18 * q^19 + 9 * q^20 - 9 * q^21 - 12 * q^22 + 57 * q^23 - 18 * q^24 - 3 * q^25 - 27 * q^26 + 27 * q^27 - 33 * q^28 + 39 * q^29 - 18 * q^30 + 27 * q^31 - 42 * q^32 - 9 * q^33 - 52 * q^34 + 48 * q^35 - 18 * q^36 - 34 * q^37 - 36 * q^38 - 73 * q^40 - 33 * q^41 - 63 * q^42 - 27 * q^43 - 153 * q^44 - 90 * q^45 - 117 * q^46 - 99 * q^47 - 117 * q^48 - 83 * q^49 - 222 * q^50 - 63 * q^51 - 91 * q^52 - 174 * q^53 - 144 * q^54 - 90 * q^55 - 243 * q^56 - 90 * q^57 - 91 * q^58 - 123 * q^59 - 135 * q^60 - 97 * q^61 - 207 * q^62 - 54 * q^63 - 119 * q^64 - 171 * q^65 - 90 * q^66 - 9 * q^67 - 114 * q^68 - 126 * q^69 - 81 * q^70 - 60 * q^71 - 18 * q^72 - 73 * q^73 - 39 * q^74 - 90 * q^75 - 66 * q^76 - 117 * q^77 + 9 * q^78 + 57 * q^79 - 108 * q^81 - 34 * q^82 - 27 * q^83 - 45 * q^84 - 68 * q^85 + 12 * q^86 - 144 * q^87 + 60 * q^88 - 105 * q^89 + 45 * q^90 - 15 * q^91 + 195 * q^92 - 234 * q^93 + 75 * q^94 - 132 * q^95 + 99 * q^96 - 79 * q^97 + 333 * q^98 - 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)

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
324.2.a	\(\chi_{324}(1, \cdot)\)	324.2.a.a	1	1
		324.2.a.b	1
		324.2.a.c	1
		324.2.a.d	1
324.2.b	\(\chi_{324}(323, \cdot)\)	324.2.b.a	4	1
		324.2.b.b	8
		324.2.b.c	8
324.2.e	\(\chi_{324}(109, \cdot)\)	324.2.e.a	2	2
		324.2.e.b	2
		324.2.e.c	2
		324.2.e.d	2
324.2.h	\(\chi_{324}(107, \cdot)\)	324.2.h.a	4	2
		324.2.h.b	4
		324.2.h.c	4
		324.2.h.d	8
		324.2.h.e	8
		324.2.h.f	16
324.2.i	\(\chi_{324}(37, \cdot)\)	324.2.i.a	18	6
324.2.l	\(\chi_{324}(35, \cdot)\)	324.2.l.a	96	6
324.2.m	\(\chi_{324}(13, \cdot)\)	324.2.m.a	162	18
324.2.p	\(\chi_{324}(11, \cdot)\)	324.2.p.a	936	18

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(324))\) into lower level spaces

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