Properties

Label 48.16
Level 48
Weight 16
Dimension 401
Nonzero newspaces 4
Sturm bound 2048
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(2048\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(48))\).

Total New Old
Modular forms 988 409 579
Cusp forms 932 401 531
Eisenstein series 56 8 48

Trace form

\( 401 q - 2189 q^{3} + 97896 q^{4} + 136762 q^{5} - 1712852 q^{6} - 764040 q^{7} - 22726956 q^{8} + 83180685 q^{9} + O(q^{10}) \) \( 401 q - 2189 q^{3} + 97896 q^{4} + 136762 q^{5} - 1712852 q^{6} - 764040 q^{7} - 22726956 q^{8} + 83180685 q^{9} + 26528 q^{10} - 281358300 q^{11} - 11982248 q^{12} - 253157126 q^{13} + 1630297860 q^{14} + 1708593750 q^{15} + 1646188496 q^{16} + 728554814 q^{17} + 5871858928 q^{18} + 6968453312 q^{19} + 21351250000 q^{20} + 21841447564 q^{21} - 92057442248 q^{22} - 59429702200 q^{23} - 64393973652 q^{24} - 27218659361 q^{25} - 30752852020 q^{26} - 137902140953 q^{27} + 105593079680 q^{28} - 81842043982 q^{29} + 38659881340 q^{30} - 402062199408 q^{31} - 896932384320 q^{32} + 213476030528 q^{33} + 2526110544776 q^{34} - 512582824200 q^{35} - 1820636115184 q^{36} - 1647558879326 q^{37} + 3704539228456 q^{38} + 1986450773762 q^{39} - 1130596394424 q^{40} - 1510889291082 q^{41} + 3146651583276 q^{42} - 1292152055696 q^{43} + 4766423343032 q^{44} + 10139747944014 q^{45} - 5810374014912 q^{46} - 5755018344192 q^{47} + 1233080713632 q^{48} + 73351610900069 q^{49} + 27463002405348 q^{50} + 7694940877866 q^{51} - 88240155448144 q^{52} - 10859571358966 q^{53} + 38965900502708 q^{54} + 50825729642208 q^{55} - 2697494479680 q^{56} - 41291338044216 q^{57} - 39975837708600 q^{58} + 40837556090860 q^{59} - 26544128112424 q^{60} + 134597273441434 q^{61} + 65640448052412 q^{62} - 35166186484344 q^{63} - 535568615852352 q^{64} - 29873192877492 q^{65} + 119407670610604 q^{66} + 447394294488608 q^{67} + 134752658650976 q^{68} - 336498348707300 q^{69} - 583737877282792 q^{70} + 286112496984760 q^{71} - 650505105387356 q^{72} - 78857250361294 q^{73} + 762109812337324 q^{74} - 522892134165919 q^{75} - 521490277220880 q^{76} - 327033767238992 q^{77} - 337247883415368 q^{78} + 1498120571803760 q^{79} - 398529240002488 q^{80} - 2032587788661103 q^{81} + 1349874510840920 q^{82} - 1319791570523316 q^{83} - 1627791203171240 q^{84} - 825461634473628 q^{85} - 141244893536560 q^{86} + 2701674175534746 q^{87} + 1755589272083264 q^{88} + 781183023982230 q^{89} + 1253972893910840 q^{90} - 4190194366337408 q^{91} - 1901815334846032 q^{92} + 437857685361976 q^{93} + 4681242437827912 q^{94} + 1040445668593864 q^{95} + 5315444092603528 q^{96} - 558247037867342 q^{97} - 8872215016606552 q^{98} - 4785239645992720 q^{99} + O(q^{100}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.16.a \(\chi_{48}(1, \cdot)\) 48.16.a.a 1 1
48.16.a.b 1
48.16.a.c 1
48.16.a.d 1
48.16.a.e 1
48.16.a.f 1
48.16.a.g 1
48.16.a.h 2
48.16.a.i 2
48.16.a.j 2
48.16.a.k 2
48.16.c \(\chi_{48}(47, \cdot)\) 48.16.c.a 2 1
48.16.c.b 4
48.16.c.c 4
48.16.c.d 20
48.16.d \(\chi_{48}(25, \cdot)\) None 0 1
48.16.f \(\chi_{48}(23, \cdot)\) None 0 1
48.16.j \(\chi_{48}(13, \cdot)\) n/a 120 2
48.16.k \(\chi_{48}(11, \cdot)\) n/a 236 2

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

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