Space of modular forms of level 18 and weight 14

• Label: 18.14
• Level: 18
• Weight: 14
• Dimension: 31
• Nonzero newspaces: 2
• Newform subspaces: 7
• Sturm bound: 252
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(252\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(18))\).

	Total	New	Old
Modular forms	125	31	94
Cusp forms	109	31	78
Eisenstein series	16	0	16

Trace form

31 * q - 128 * q^2 + 1329 * q^3 - 32768 * q^4 - 74202 * q^5 + 60096 * q^6 + 191462 * q^7 + 262144 * q^8 - 2736825 * q^9 + 1605504 * q^10 - 8620893 * q^11 + 3833856 * q^12 + 29280716 * q^13 - 50819968 * q^14 - 99624816 * q^15 - 134217728 * q^16 + 203935836 * q^17 - 208977792 * q^18 + 506829386 * q^19 - 303931392 * q^20 + 937482990 * q^21 + 587851200 * q^22 + 2725959294 * q^23 - 614203392 * q^24 - 2075219636 * q^25 + 5005236608 * q^26 + 3685317264 * q^27 - 1523728384 * q^28 - 16387571952 * q^29 + 8688909312 * q^30 + 15540317348 * q^31 - 2147483648 * q^32 - 32409465885 * q^33 + 652687680 * q^34 + 43302344208 * q^35 + 9340612608 * q^36 - 22597387258 * q^37 - 33179543488 * q^38 + 1188361512 * q^39 + 6576144384 * q^40 + 54259141413 * q^41 - 3100930560 * q^42 - 75163656799 * q^43 - 60819480576 * q^44 - 69754275576 * q^45 + 116893101312 * q^46 + 272512448238 * q^47 - 38000394240 * q^48 - 419654375820 * q^49 - 220585910912 * q^50 + 475083483453 * q^51 + 119933812736 * q^52 - 485578241346 * q^53 + 60065349696 * q^54 + 178127312472 * q^55 - 208158588928 * q^56 - 882692482353 * q^57 + 369923622912 * q^58 - 145317428091 * q^59 + 389234294784 * q^60 - 37254394738 * q^61 - 223157175808 * q^62 + 664630330308 * q^63 + 2130303778816 * q^64 - 671713584924 * q^65 - 952790860800 * q^66 + 1362536620115 * q^67 - 276450865152 * q^68 - 1410213836160 * q^69 - 497341104384 * q^70 + 6696077341296 * q^71 + 2230328229888 * q^72 + 2099245503320 * q^73 - 3104065596544 * q^74 - 2410698689403 * q^75 - 1439225245696 * q^76 - 8574476624298 * q^77 - 3538835698560 * q^78 + 8842084143068 * q^79 + 2429709975552 * q^80 + 10563831408339 * q^81 - 1553024626944 * q^82 - 23995523373936 * q^83 - 3184082313216 * q^84 - 8225282491020 * q^85 - 3217522851520 * q^86 + 11924718603354 * q^87 + 2407838515200 * q^88 + 20079085826046 * q^89 + 15271725878784 * q^90 + 4163364688120 * q^91 + 11165529268224 * q^92 - 71102462144400 * q^93 - 23301423954816 * q^94 - 23853919858032 * q^95 + 1507533520896 * q^96 + 27652307459969 * q^97 + 34789889051712 * q^98 + 72403854987186 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.14.a	\(\chi_{18}(1, \cdot)\)	18.14.a.a	1	1
		18.14.a.b	1
		18.14.a.c	1
		18.14.a.d	1
		18.14.a.e	1
18.14.c	\(\chi_{18}(7, \cdot)\)	18.14.c.a	12	2
		18.14.c.b	14

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)