Space of modular forms of level 54 and weight 7

• Label: 54.7
• Level: 54
• Weight: 7
• Dimension: 128
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 1134
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1134\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(54))\).

	Total	New	Old
Modular forms	516	128	388
Cusp forms	456	128	328
Eisenstein series	60	0	60

Trace form

128 * q - 64 * q^4 - 864 * q^5 + 336 * q^6 + 1444 * q^7 - 2496 * q^9 - 1824 * q^10 - 756 * q^11 + 960 * q^12 + 868 * q^13 + 9504 * q^14 + 5112 * q^15 + 2048 * q^16 - 22080 * q^18 - 18644 * q^19 + 13824 * q^20 + 16080 * q^21 + 14784 * q^22 + 16416 * q^23 + 57458 * q^25 + 3078 * q^27 - 23168 * q^28 + 58536 * q^29 + 149184 * q^30 + 52276 * q^31 - 57294 * q^33 + 42912 * q^34 - 536544 * q^35 - 120576 * q^36 - 197060 * q^37 + 148176 * q^38 + 81696 * q^39 + 58368 * q^40 + 353916 * q^41 + 222528 * q^42 + 177916 * q^43 + 327132 * q^45 - 154176 * q^46 - 1069524 * q^47 - 98304 * q^48 - 111162 * q^49 - 622080 * q^50 - 1066716 * q^51 - 27776 * q^52 + 372240 * q^54 + 693396 * q^55 + 304128 * q^56 + 1674126 * q^57 + 420576 * q^58 + 486378 * q^59 + 354816 * q^60 - 51908 * q^61 - 1675032 * q^63 + 1114112 * q^64 - 3695112 * q^65 - 786240 * q^66 + 928156 * q^67 - 997056 * q^68 + 3773592 * q^69 + 741552 * q^70 + 855360 * q^71 - 233472 * q^72 + 2309404 * q^73 + 1340928 * q^74 - 1831308 * q^75 - 454592 * q^76 - 6203088 * q^77 - 2385792 * q^78 - 3686756 * q^79 + 3791448 * q^81 + 523776 * q^82 + 3042360 * q^83 - 283392 * q^84 + 4627800 * q^85 - 1734048 * q^86 + 5122692 * q^87 + 563712 * q^88 - 964710 * q^89 + 469440 * q^90 + 1235240 * q^91 + 1914624 * q^92 - 4105752 * q^93 - 1735824 * q^94 + 231552 * q^95 - 491520 * q^96 + 2565580 * q^97 + 4393440 * q^98 + 3499164 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(54))\)

We only show spaces with odd 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
54.7.b	\(\chi_{54}(53, \cdot)\)	54.7.b.a	2	1
		54.7.b.b	2
		54.7.b.c	4
54.7.d	\(\chi_{54}(17, \cdot)\)	54.7.d.a	12	2
54.7.f	\(\chi_{54}(5, \cdot)\)	54.7.f.a	108	6

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(54)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)