Space of modular forms of level 270 and weight 2

• Label: 270.2
• Level: 270
• Weight: 2
• Dimension: 468
• Nonzero newspaces: 9
• Newform subspaces: 23
• Sturm bound: 7776
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 23 \)
Sturm bound:			\(7776\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(270))\).

	Total	New	Old
Modular forms	2184	468	1716
Cusp forms	1705	468	1237
Eisenstein series	479	0	479

Trace form

468 * q - 2 * q^2 - 2 * q^4 + 6 * q^5 + 12 * q^6 + 8 * q^7 + 10 * q^8 + 24 * q^9 + 14 * q^10 + 52 * q^11 + 6 * q^12 + 36 * q^13 + 24 * q^14 + 18 * q^15 - 2 * q^16 + 36 * q^17 - 12 * q^18 + 12 * q^19 - 4 * q^20 - 48 * q^21 + 8 * q^22 - 12 * q^23 + 26 * q^25 - 64 * q^26 - 54 * q^27 - 4 * q^28 - 48 * q^29 - 36 * q^30 + 24 * q^31 - 2 * q^32 - 78 * q^33 - 20 * q^34 - 102 * q^35 - 36 * q^36 - 24 * q^37 - 94 * q^38 - 36 * q^39 - 26 * q^40 - 140 * q^41 - 48 * q^42 - 72 * q^43 - 40 * q^44 - 120 * q^45 - 48 * q^46 - 180 * q^47 - 12 * q^48 - 66 * q^49 - 114 * q^50 - 96 * q^51 - 12 * q^52 - 96 * q^53 - 14 * q^55 - 32 * q^56 - 54 * q^57 + 4 * q^58 - 26 * q^59 + 18 * q^60 + 52 * q^61 + 56 * q^62 + 12 * q^63 + 10 * q^64 + 50 * q^65 - 52 * q^67 + 54 * q^68 - 36 * q^69 - 10 * q^70 - 48 * q^72 + 28 * q^73 - 12 * q^74 - 24 * q^75 - 14 * q^76 - 168 * q^77 - 72 * q^78 - 240 * q^79 - 12 * q^80 - 96 * q^81 - 28 * q^82 - 168 * q^83 - 120 * q^85 + 4 * q^86 - 192 * q^87 - 46 * q^88 - 130 * q^89 - 18 * q^90 - 60 * q^91 + 24 * q^92 - 132 * q^93 - 28 * q^94 - 142 * q^95 - 12 * q^96 - 72 * q^97 + 66 * q^98 - 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)

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
270.2.a	\(\chi_{270}(1, \cdot)\)	270.2.a.a	1	1
		270.2.a.b	1
		270.2.a.c	1
		270.2.a.d	1
270.2.c	\(\chi_{270}(109, \cdot)\)	270.2.c.a	2	1
		270.2.c.b	2
		270.2.c.c	4
270.2.e	\(\chi_{270}(91, \cdot)\)	270.2.e.a	2	2
		270.2.e.b	2
		270.2.e.c	4
270.2.f	\(\chi_{270}(53, \cdot)\)	270.2.f.a	8	2
		270.2.f.b	8
270.2.i	\(\chi_{270}(19, \cdot)\)	270.2.i.a	4	2
		270.2.i.b	8
270.2.k	\(\chi_{270}(31, \cdot)\)	270.2.k.a	6	6
		270.2.k.b	12
		270.2.k.c	12
		270.2.k.d	18
		270.2.k.e	24
270.2.m	\(\chi_{270}(17, \cdot)\)	270.2.m.a	8	4
		270.2.m.b	16
270.2.p	\(\chi_{270}(49, \cdot)\)	270.2.p.a	108	6
270.2.r	\(\chi_{270}(23, \cdot)\)	270.2.r.a	216	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(270))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(270)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)