Space of modular forms of level 69 and weight 4

• Label: 69.4
• Level: 69
• Weight: 4
• Dimension: 374
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 1408
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1408\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(69))\).

	Total	New	Old
Modular forms	572	418	154
Cusp forms	484	374	110
Eisenstein series	88	44	44

Trace form

374 * q - 11 * q^3 - 22 * q^4 - 11 * q^6 - 22 * q^7 - 11 * q^9 - 22 * q^10 - 11 * q^12 - 22 * q^13 + 363 * q^15 + 858 * q^16 + 176 * q^17 - 99 * q^18 - 242 * q^19 - 1408 * q^20 - 671 * q^21 - 968 * q^22 - 968 * q^23 - 1342 * q^24 - 726 * q^25 - 440 * q^26 - 77 * q^27 + 682 * q^28 + 440 * q^29 + 1485 * q^30 + 1078 * q^31 + 2992 * q^32 + 957 * q^33 + 3806 * q^34 + 2860 * q^35 + 979 * q^36 + 2354 * q^37 + 1210 * q^38 - 143 * q^39 - 2662 * q^40 - 1100 * q^41 - 3641 * q^42 - 3454 * q^43 - 6622 * q^44 - 7942 * q^46 - 3784 * q^47 - 3355 * q^48 - 4378 * q^49 - 3850 * q^50 - 671 * q^51 - 682 * q^52 + 484 * q^53 - 2541 * q^54 + 3938 * q^55 + 7150 * q^56 + 1705 * q^57 + 12188 * q^58 + 6028 * q^59 + 3179 * q^60 - 22 * q^61 + 2079 * q^63 - 22 * q^64 + 5742 * q^66 - 22 * q^67 + 3729 * q^69 - 44 * q^70 + 7381 * q^72 - 22 * q^73 + 4730 * q^74 + 9955 * q^75 + 16368 * q^76 + 10472 * q^77 + 8547 * q^78 + 5698 * q^79 + 8118 * q^80 - 1375 * q^81 - 154 * q^82 - 1672 * q^83 - 16753 * q^84 - 10802 * q^85 - 13420 * q^86 - 9383 * q^87 - 12518 * q^88 - 11220 * q^89 - 18700 * q^90 - 16016 * q^91 - 18018 * q^92 - 11770 * q^93 - 16676 * q^94 - 8052 * q^95 - 5522 * q^96 + 4598 * q^97 + 5280 * q^98 - 1859 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)

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
69.4.a	\(\chi_{69}(1, \cdot)\)	69.4.a.a	2	1
		69.4.a.b	2
		69.4.a.c	4
		69.4.a.d	4
69.4.c	\(\chi_{69}(68, \cdot)\)	69.4.c.a	2	1
		69.4.c.b	4
		69.4.c.c	16
69.4.e	\(\chi_{69}(4, \cdot)\)	69.4.e.a	60	10
		69.4.e.b	60
69.4.g	\(\chi_{69}(5, \cdot)\)	69.4.g.a	220	10

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces

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