Space of modular forms of level 297 and weight 2

• Label: 297.2
• Level: 297
• Weight: 2
• Dimension: 2374
• Nonzero newspaces: 12
• Newform subspaces: 33
• Sturm bound: 12960
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 33 \)
Sturm bound:			\(12960\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(297))\).

	Total	New	Old
Modular forms	3540	2662	878
Cusp forms	2941	2374	567
Eisenstein series	599	288	311

Trace form

2374 * q - 28 * q^2 - 48 * q^3 - 54 * q^4 - 34 * q^5 - 60 * q^6 - 56 * q^7 - 52 * q^8 - 60 * q^9 - 64 * q^10 - 43 * q^11 - 144 * q^12 - 68 * q^13 - 70 * q^14 - 78 * q^15 - 78 * q^16 - 58 * q^17 - 78 * q^18 - 50 * q^19 - 54 * q^20 - 36 * q^21 - 73 * q^22 - 66 * q^23 - 24 * q^24 - 86 * q^25 - 20 * q^26 - 42 * q^27 - 200 * q^28 - 58 * q^29 - 42 * q^30 - 88 * q^31 - 120 * q^32 - 60 * q^33 - 198 * q^34 - 114 * q^35 - 96 * q^36 - 106 * q^37 - 184 * q^38 - 126 * q^39 - 172 * q^40 - 100 * q^41 - 96 * q^42 - 112 * q^43 - 73 * q^44 - 102 * q^45 - 64 * q^46 - 10 * q^47 - 30 * q^48 - 82 * q^49 - 24 * q^50 - 24 * q^51 - 108 * q^52 - 44 * q^53 + 48 * q^54 - 188 * q^55 - 114 * q^56 - 54 * q^57 - 192 * q^58 - 86 * q^59 - 60 * q^60 - 132 * q^61 - 166 * q^62 - 78 * q^63 - 158 * q^64 - 136 * q^65 - 51 * q^66 - 200 * q^67 - 208 * q^68 - 78 * q^69 - 160 * q^70 - 174 * q^71 - 96 * q^72 - 108 * q^73 - 246 * q^74 - 138 * q^75 - 82 * q^76 - 135 * q^77 - 156 * q^78 - 60 * q^79 + 196 * q^80 - 72 * q^81 - 116 * q^82 + 22 * q^83 + 168 * q^84 + 144 * q^85 + 188 * q^86 + 72 * q^87 + 280 * q^88 + 152 * q^89 + 204 * q^90 + 48 * q^91 + 598 * q^92 + 168 * q^93 + 280 * q^94 + 426 * q^95 + 420 * q^96 + 122 * q^97 + 550 * q^98 + 207 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)

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
297.2.a	\(\chi_{297}(1, \cdot)\)	297.2.a.a	1	1
		297.2.a.b	1
		297.2.a.c	1
		297.2.a.d	1
		297.2.a.e	2
		297.2.a.f	2
		297.2.a.g	3
		297.2.a.h	3
297.2.d	\(\chi_{297}(296, \cdot)\)	297.2.d.a	8	1
		297.2.d.b	8
297.2.e	\(\chi_{297}(100, \cdot)\)	297.2.e.a	2	2
		297.2.e.b	2
		297.2.e.c	2
		297.2.e.d	6
		297.2.e.e	8
297.2.f	\(\chi_{297}(82, \cdot)\)	297.2.f.a	16	4
		297.2.f.b	16
		297.2.f.c	16
		297.2.f.d	16
297.2.g	\(\chi_{297}(98, \cdot)\)	297.2.g.a	4	2
		297.2.g.b	16
297.2.j	\(\chi_{297}(34, \cdot)\)	297.2.j.a	6	6
		297.2.j.b	72
		297.2.j.c	102
297.2.k	\(\chi_{297}(107, \cdot)\)	297.2.k.a	32	4
		297.2.k.b	32
297.2.n	\(\chi_{297}(37, \cdot)\)	297.2.n.a	8	8
		297.2.n.b	72
297.2.o	\(\chi_{297}(32, \cdot)\)	297.2.o.a	12	6
		297.2.o.b	192
297.2.t	\(\chi_{297}(8, \cdot)\)	297.2.t.a	80	8
297.2.u	\(\chi_{297}(4, \cdot)\)	297.2.u.a	816	24
297.2.x	\(\chi_{297}(2, \cdot)\)	297.2.x.a	816	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(297))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(297)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)