Space of modular forms of level 207 and weight 4

• Label: 207.4
• Level: 207
• Weight: 4
• Dimension: 3653
• Nonzero newspaces: 8
• Newform subspaces: 20
• Sturm bound: 12672
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 20 \)
Sturm bound:			\(12672\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(207))\).

	Total	New	Old
Modular forms	4928	3841	1087
Cusp forms	4576	3653	923
Eisenstein series	352	188	164

Trace form

3653 * q - 27 * q^2 - 38 * q^3 - 7 * q^4 - 3 * q^5 - 62 * q^6 - 59 * q^7 - 165 * q^8 - 134 * q^9 - 123 * q^10 + 99 * q^11 + 268 * q^12 + 85 * q^13 + 87 * q^14 - 98 * q^15 - 615 * q^16 - 517 * q^17 - 476 * q^18 + 207 * q^19 + 647 * q^20 - 86 * q^21 + 374 * q^22 + 484 * q^23 + 110 * q^24 + 327 * q^25 + 1243 * q^26 + 820 * q^27 - 795 * q^28 - 355 * q^29 - 620 * q^30 - 1113 * q^31 - 2375 * q^32 - 440 * q^33 - 1353 * q^34 - 1475 * q^35 + 406 * q^36 - 1307 * q^37 - 1760 * q^38 - 1562 * q^39 + 1815 * q^40 + 781 * q^41 + 928 * q^42 + 2899 * q^43 + 4466 * q^44 + 1306 * q^45 + 4389 * q^46 + 2624 * q^47 - 2 * q^48 + 1005 * q^49 + 1034 * q^50 - 638 * q^51 - 2363 * q^52 - 491 * q^53 + 3774 * q^54 + 2937 * q^55 + 13948 * q^56 + 6622 * q^57 - 714 * q^58 + 1453 * q^59 + 908 * q^60 - 1103 * q^61 - 5637 * q^62 - 5430 * q^63 - 8839 * q^64 - 12639 * q^65 - 8976 * q^66 - 653 * q^67 - 25542 * q^68 - 8415 * q^69 - 16854 * q^70 - 15735 * q^71 - 16610 * q^72 - 3827 * q^73 - 10798 * q^74 - 3322 * q^75 - 13558 * q^76 - 4939 * q^77 + 4840 * q^78 - 723 * q^79 + 16644 * q^80 + 8834 * q^81 + 7755 * q^82 + 16487 * q^83 + 21376 * q^84 + 20009 * q^85 + 22451 * q^86 + 262 * q^87 + 8657 * q^88 + 7161 * q^89 + 1644 * q^90 + 13822 * q^91 + 8118 * q^92 + 338 * q^93 + 12494 * q^94 + 3729 * q^95 - 796 * q^96 + 1789 * q^97 - 981 * q^98 - 638 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)

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
207.4.a	\(\chi_{207}(1, \cdot)\)	207.4.a.a	1	1
		207.4.a.b	2
		207.4.a.c	2
		207.4.a.d	4
		207.4.a.e	4
		207.4.a.f	4
		207.4.a.g	5
		207.4.a.h	5
207.4.c	\(\chi_{207}(206, \cdot)\)	207.4.c.a	24	1
207.4.e	\(\chi_{207}(70, \cdot)\)	207.4.e.a	60	2
		207.4.e.b	72
207.4.g	\(\chi_{207}(68, \cdot)\)	207.4.g.a	12	2
		207.4.g.b	128
207.4.i	\(\chi_{207}(55, \cdot)\)	207.4.i.a	50	10
		207.4.i.b	60
		207.4.i.c	60
		207.4.i.d	120
207.4.k	\(\chi_{207}(17, \cdot)\)	207.4.k.a	240	10
207.4.m	\(\chi_{207}(4, \cdot)\)	207.4.m.a	1400	20
207.4.o	\(\chi_{207}(5, \cdot)\)	207.4.o.a	1400	20

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(207))\) into lower level spaces

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