Space of modular forms of level 48 and weight 18

• Label: 48.18
• Level: 48
• Weight: 18
• Dimension: 455
• Nonzero newspaces: 4
• Sturm bound: 2304
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	=	\( 18 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(2304\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(48))\).

	Total	New	Old
Modular forms	1116	463	653
Cusp forms	1060	455	605
Eisenstein series	56	8	48

Trace form

455 * q + 6559 * q^3 + 109480 * q^4 + 24478 * q^5 + 9659404 * q^6 - 18920328 * q^7 + 203064468 * q^8 + 492169323 * q^9 - 568330656 * q^10 - 26660748 * q^11 - 647301320 * q^12 + 1368990550 * q^13 - 13160947644 * q^14 - 25628906250 * q^15 - 45972879024 * q^16 - 7489125598 * q^17 + 8544294928 * q^18 + 248979344240 * q^19 - 390368750000 * q^20 - 384578948924 * q^21 - 1009240462024 * q^22 + 809469569288 * q^23 + 1256182602348 * q^24 - 3812206219175 * q^25 - 3622860188980 * q^26 + 3614810806891 * q^27 + 1292651940480 * q^28 + 3573845782166 * q^29 + 15835780496860 * q^30 + 14779377665168 * q^31 - 8013385766400 * q^32 + 25707471874232 * q^33 - 30518789279608 * q^34 + 62828949772824 * q^35 + 9593875765904 * q^36 + 94104580888126 * q^37 - 93635031110168 * q^38 + 62628166108946 * q^39 + 58388430456776 * q^40 + 34757875502106 * q^41 - 97584022854804 * q^42 + 104140120940160 * q^43 - 236582530242184 * q^44 - 120612819292782 * q^45 + 211607589721600 * q^46 + 232614811457280 * q^47 - 157208555265504 * q^48 + 2289301756329923 * q^49 + 565065504246372 * q^50 + 276138999589218 * q^51 - 1259229170804112 * q^52 + 2765365498269614 * q^53 + 260336701058612 * q^54 - 4675236097738720 * q^55 - 2390376488672256 * q^56 + 3389598761843832 * q^57 + 7910815391809096 * q^58 - 2615718154535780 * q^59 - 3245091079537384 * q^60 - 235780034738538 * q^61 + 2267579600947068 * q^62 + 1170788505869448 * q^63 + 13111307274356032 * q^64 + 524782976386356 * q^65 - 21673799416025588 * q^66 - 14113737713199984 * q^67 + 37045007994380192 * q^68 + 10317604524808732 * q^69 - 19699061906896872 * q^70 + 7629530017252600 * q^71 + 14697211694768356 * q^72 + 14836526711523710 * q^73 + 46968569186626540 * q^74 + 36681660490590989 * q^75 - 61010868480453968 * q^76 - 41531359828511984 * q^77 + 126131277122034648 * q^78 - 26038089719192976 * q^79 - 80032180076115832 * q^80 - 272906888040448969 * q^81 - 73170622855857256 * q^82 + 162191500634540124 * q^83 + 111246202638630808 * q^84 - 32732039709499316 * q^85 - 37450351670844976 * q^86 - 43810968044169654 * q^87 - 38987409314242752 * q^88 - 35392862392888038 * q^89 - 128321616762944968 * q^90 - 20332198747929408 * q^91 + 481247177697072944 * q^92 + 68352524312934064 * q^93 - 211619668790440504 * q^94 + 309431441968212424 * q^95 - 409907714157606008 * q^96 + 279165508176630846 * q^97 + 421800470476794920 * q^98 + 253556724500322368 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.18.a	\(\chi_{48}(1, \cdot)\)	48.18.a.a	1	1
		48.18.a.b	1
		48.18.a.c	1
		48.18.a.d	1
		48.18.a.e	1
		48.18.a.f	1
		48.18.a.g	2
		48.18.a.h	2
		48.18.a.i	2
		48.18.a.j	2
		48.18.a.k	3
48.18.c	\(\chi_{48}(47, \cdot)\)	48.18.c.a	2	1
		48.18.c.b	12
		48.18.c.c	20
48.18.d	\(\chi_{48}(25, \cdot)\)	None	0	1
48.18.f	\(\chi_{48}(23, \cdot)\)	None	0	1
48.18.j	\(\chi_{48}(13, \cdot)\)	n/a	136	2
48.18.k	\(\chi_{48}(11, \cdot)\)	n/a	268	2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)