Space of modular forms of level 207 and weight 2

• Label: 207.2
• Level: 207
• Weight: 2
• Dimension: 1155
• Nonzero newspaces: 8
• Newform subspaces: 18
• Sturm bound: 6336
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(6336\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(207))\).

	Total	New	Old
Modular forms	1760	1343	417
Cusp forms	1409	1155	254
Eisenstein series	351	188	163

Trace form

1155 * q - 33 * q^2 - 44 * q^3 - 33 * q^4 - 33 * q^5 - 44 * q^6 - 33 * q^7 - 33 * q^8 - 44 * q^9 - 99 * q^10 - 33 * q^11 - 44 * q^12 - 33 * q^13 - 33 * q^14 - 44 * q^15 - 55 * q^16 - 44 * q^17 - 44 * q^18 - 110 * q^19 - 77 * q^20 - 44 * q^21 - 66 * q^22 - 55 * q^23 - 88 * q^24 - 55 * q^25 - 55 * q^26 - 44 * q^27 - 143 * q^28 - 44 * q^29 - 44 * q^30 - 44 * q^31 - 55 * q^32 - 44 * q^33 - 55 * q^34 - 55 * q^35 - 44 * q^36 - 143 * q^37 - 88 * q^38 - 44 * q^39 - 121 * q^40 - 55 * q^41 - 44 * q^42 - 77 * q^43 - 44 * q^44 - 44 * q^45 - 187 * q^46 - 110 * q^47 - 44 * q^48 - 99 * q^49 - 110 * q^50 - 44 * q^51 - 143 * q^52 - 55 * q^53 - 77 * q^55 + 110 * q^56 + 22 * q^57 + 44 * q^58 + 77 * q^59 + 176 * q^60 + 99 * q^61 + 165 * q^62 + 66 * q^63 + 165 * q^64 + 198 * q^65 + 132 * q^66 + 33 * q^67 + 396 * q^68 + 66 * q^69 + 198 * q^70 + 132 * q^71 + 220 * q^72 - 33 * q^73 + 220 * q^74 + 110 * q^75 + 176 * q^76 + 88 * q^77 + 88 * q^78 + 55 * q^79 + 198 * q^80 + 44 * q^81 - 33 * q^82 + 22 * q^83 + 88 * q^84 - 77 * q^85 - 77 * q^86 - 44 * q^87 - 165 * q^88 - 99 * q^89 - 198 * q^91 - 132 * q^92 - 88 * q^93 - 154 * q^94 - 132 * q^95 + 44 * q^96 - 132 * q^97 - 165 * q^98 - 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)

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
207.2.a	\(\chi_{207}(1, \cdot)\)	207.2.a.a	1	1
		207.2.a.b	2
		207.2.a.c	2
		207.2.a.d	2
		207.2.a.e	2
207.2.c	\(\chi_{207}(206, \cdot)\)	207.2.c.a	8	1
207.2.e	\(\chi_{207}(70, \cdot)\)	207.2.e.a	16	2
		207.2.e.b	28
207.2.g	\(\chi_{207}(68, \cdot)\)	207.2.g.a	12	2
		207.2.g.b	32
207.2.i	\(\chi_{207}(55, \cdot)\)	207.2.i.a	10	10
		207.2.i.b	10
		207.2.i.c	10
		207.2.i.d	20
		207.2.i.e	40
207.2.k	\(\chi_{207}(17, \cdot)\)	207.2.k.a	80	10
207.2.m	\(\chi_{207}(4, \cdot)\)	207.2.m.a	440	20
207.2.o	\(\chi_{207}(5, \cdot)\)	207.2.o.a	440	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(207))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(207)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)