Space of modular forms of level 18 and weight 7

• Label: 18.7
• Level: 18
• Weight: 7
• Dimension: 14
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 126
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(126\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(18))\).

	Total	New	Old
Modular forms	62	14	48
Cusp forms	46	14	32
Eisenstein series	16	0	16

Trace form

14 * q - 42 * q^3 + 128 * q^4 + 432 * q^5 - 144 * q^6 - 728 * q^7 + 2190 * q^9 - 1968 * q^10 + 378 * q^11 + 384 * q^12 + 8416 * q^13 - 4752 * q^14 - 10872 * q^15 - 4096 * q^16 - 2976 * q^18 + 8668 * q^19 + 13824 * q^20 + 24876 * q^21 - 18768 * q^22 - 76248 * q^23 - 6144 * q^24 - 21172 * q^25 + 127008 * q^27 + 46336 * q^28 + 97092 * q^29 + 34272 * q^30 - 58112 * q^31 - 246258 * q^33 - 27504 * q^34 + 38208 * q^36 + 79516 * q^37 + 97632 * q^38 + 42204 * q^39 + 62976 * q^40 - 410562 * q^41 - 222144 * q^42 + 79030 * q^43 + 13716 * q^45 - 96864 * q^46 + 347652 * q^47 + 55296 * q^48 + 97260 * q^49 + 311040 * q^50 + 336402 * q^51 - 269312 * q^52 - 173520 * q^54 + 113976 * q^55 - 152064 * q^56 - 522282 * q^57 - 172848 * q^58 + 369738 * q^59 - 170496 * q^60 + 162244 * q^61 - 103800 * q^63 - 458752 * q^64 - 753840 * q^65 + 909216 * q^66 + 47998 * q^67 + 744768 * q^68 + 2059272 * q^69 + 1108464 * q^70 - 374784 * q^72 - 505412 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 412736 * q^76 - 159192 * q^77 - 631488 * q^78 - 835028 * q^79 - 1428282 * q^81 + 1492176 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1615140 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 600576 * q^88 - 1987200 * q^90 - 2904640 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 1605648 * q^94 - 2089260 * q^95 - 49152 * q^96 - 681722 * q^97 + 4398804 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.7.b	\(\chi_{18}(17, \cdot)\)	18.7.b.a	2	1
18.7.d	\(\chi_{18}(5, \cdot)\)	18.7.d.a	12	2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

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