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Properties

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

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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

\( 455 q + 6559 q^{3} + 109480 q^{4} + 24478 q^{5} + 9659404 q^{6} - 18920328 q^{7} + 203064468 q^{8} + 492169323 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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