Space of modular forms of level 294 and weight 2

• Label: 294.2
• Level: 294
• Weight: 2
• Dimension: 563
• Nonzero newspaces: 8
• Newform subspaces: 28
• Sturm bound: 9408
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(9408\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(294))\).

	Total	New	Old
Modular forms	2592	563	2029
Cusp forms	2113	563	1550
Eisenstein series	479	0	479

Trace form

563 * q - q^2 + 3 * q^3 + 7 * q^4 + 18 * q^5 + 11 * q^6 + 16 * q^7 - q^8 + 15 * q^9 + 18 * q^10 + 36 * q^11 + 3 * q^12 + 18 * q^13 - 6 * q^15 - q^16 + 6 * q^17 - 25 * q^18 + 12 * q^19 - 6 * q^20 - 10 * q^21 - 12 * q^22 - 13 * q^24 + 17 * q^25 + 10 * q^26 + 3 * q^27 + 12 * q^28 + 18 * q^29 + 18 * q^30 + 48 * q^31 - q^32 + 36 * q^33 + 30 * q^34 + 48 * q^35 + 15 * q^36 - 38 * q^37 - 32 * q^38 - 56 * q^39 - 66 * q^40 - 114 * q^41 - 54 * q^42 - 52 * q^43 - 48 * q^44 - 66 * q^45 - 180 * q^46 - 144 * q^47 - 11 * q^48 - 288 * q^49 - 103 * q^50 - 210 * q^51 - 58 * q^52 - 150 * q^53 - 37 * q^54 - 420 * q^55 - 72 * q^56 - 48 * q^57 - 222 * q^58 - 132 * q^59 - 72 * q^60 - 178 * q^61 - 68 * q^62 - 30 * q^63 + 7 * q^64 + 84 * q^65 - 12 * q^66 - 20 * q^67 + 6 * q^68 + 24 * q^69 + 72 * q^71 + 23 * q^72 + 30 * q^73 + 34 * q^74 + 45 * q^75 + 12 * q^76 + 108 * q^77 + 34 * q^78 + 160 * q^79 + 18 * q^80 + 27 * q^81 + 102 * q^82 - 12 * q^83 + 26 * q^84 + 108 * q^85 + 76 * q^86 - 78 * q^87 + 12 * q^88 - 66 * q^89 + 18 * q^90 - 56 * q^91 + 24 * q^92 - 228 * q^93 + 96 * q^94 - 240 * q^95 - 13 * q^96 - 66 * q^97 + 24 * q^98 - 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)

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
294.2.a	\(\chi_{294}(1, \cdot)\)	294.2.a.a	1	1
		294.2.a.b	1
		294.2.a.c	1
		294.2.a.d	1
		294.2.a.e	1
		294.2.a.f	1
		294.2.a.g	1
294.2.d	\(\chi_{294}(293, \cdot)\)	294.2.d.a	4	1
		294.2.d.b	8
294.2.e	\(\chi_{294}(67, \cdot)\)	294.2.e.a	2	2
		294.2.e.b	2
		294.2.e.c	2
		294.2.e.d	2
		294.2.e.e	2
		294.2.e.f	2
294.2.f	\(\chi_{294}(215, \cdot)\)	294.2.f.a	4	2
		294.2.f.b	8
		294.2.f.c	16
294.2.i	\(\chi_{294}(43, \cdot)\)	294.2.i.a	6	6
		294.2.i.b	12
		294.2.i.c	12
		294.2.i.d	18
294.2.j	\(\chi_{294}(41, \cdot)\)	294.2.j.a	120	6
294.2.m	\(\chi_{294}(25, \cdot)\)	294.2.m.a	24	12
		294.2.m.b	24
		294.2.m.c	36
		294.2.m.d	36
294.2.p	\(\chi_{294}(5, \cdot)\)	294.2.p.a	216	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(294))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(294)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)