Space of modular forms of level 18 and weight 4

• Label: 18.4
• Level: 18
• Weight: 4
• Dimension: 7
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 72
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(18))\).

	Total	New	Old
Modular forms	35	7	28
Cusp forms	19	7	12
Eisenstein series	16	0	16

Trace form

7 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 + 12 * q^5 - 18 * q^6 - 4 * q^7 - 8 * q^8 - 105 * q^9 - 12 * q^10 + 27 * q^11 + 24 * q^12 + 14 * q^13 + 68 * q^14 + 90 * q^15 - 32 * q^16 + 48 * q^17 + 156 * q^18 + 230 * q^19 + 48 * q^20 - 36 * q^21 - 42 * q^22 - 432 * q^23 - 24 * q^24 - 308 * q^25 - 316 * q^26 - 160 * q^28 - 378 * q^29 - 288 * q^30 - 94 * q^31 + 64 * q^32 + 765 * q^33 + 342 * q^34 + 1428 * q^35 + 516 * q^36 + 446 * q^37 + 362 * q^38 - 582 * q^39 - 48 * q^40 - 249 * q^41 - 816 * q^42 + 77 * q^43 - 360 * q^44 - 702 * q^45 + 168 * q^46 - 564 * q^47 - 144 * q^48 - 672 * q^49 + 436 * q^50 - 153 * q^51 + 56 * q^52 + 330 * q^53 + 954 * q^54 - 1332 * q^55 + 272 * q^56 + 987 * q^57 + 192 * q^58 + 333 * q^59 - 936 * q^60 + 320 * q^61 - 1840 * q^62 - 1794 * q^63 + 448 * q^64 + 186 * q^65 + 288 * q^66 + 2471 * q^67 + 660 * q^68 + 1494 * q^69 + 408 * q^70 - 1104 * q^71 - 24 * q^72 - 40 * q^73 + 1364 * q^74 + 3231 * q^75 - 340 * q^76 + 900 * q^77 + 132 * q^78 - 2002 * q^79 - 672 * q^80 + 315 * q^81 - 3000 * q^82 + 354 * q^83 + 744 * q^84 - 648 * q^85 - 190 * q^86 - 3204 * q^87 - 168 * q^88 - 3894 * q^89 - 432 * q^90 + 1900 * q^91 - 1728 * q^92 - 2634 * q^93 + 804 * q^94 - 2136 * q^95 + 384 * q^96 + 2183 * q^97 + 2430 * q^98 + 1152 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.4.a	\(\chi_{18}(1, \cdot)\)	18.4.a.a	1	1
18.4.c	\(\chi_{18}(7, \cdot)\)	18.4.c.a	2	2
		18.4.c.b	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

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