Properties

Label 483.3
Level 483
Weight 3
Dimension 11888
Nonzero newspaces 16
Sturm bound 50688
Trace bound 3

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Defining parameters

Level: \( N \) = \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(50688\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(483))\).

Total New Old
Modular forms 17424 12312 5112
Cusp forms 16368 11888 4480
Eisenstein series 1056 424 632

Trace form

\( 11888q - 32q^{3} - 44q^{4} + 12q^{5} - 32q^{6} - 114q^{7} + 12q^{8} + 4q^{9} + O(q^{10}) \) \( 11888q - 32q^{3} - 44q^{4} + 12q^{5} - 32q^{6} - 114q^{7} + 12q^{8} + 4q^{9} - 64q^{10} - 12q^{11} - 80q^{12} - 92q^{13} - 48q^{14} - 52q^{15} + 260q^{16} + 124q^{17} + 116q^{18} + 40q^{19} + 352q^{20} + 26q^{21} + 40q^{22} + 8q^{23} - 52q^{24} - 88q^{25} - 100q^{26} - 110q^{27} - 434q^{28} - 284q^{29} - 796q^{30} - 656q^{31} - 1036q^{32} - 658q^{33} + 400q^{34} + 20q^{35} - 110q^{36} + 1000q^{37} + 1192q^{38} + 352q^{39} + 1480q^{40} + 352q^{41} + 419q^{42} + 508q^{43} + 644q^{44} + 374q^{45} - 236q^{46} + 92q^{47} - 240q^{48} - 398q^{49} - 1312q^{50} - 236q^{51} - 3472q^{52} - 680q^{53} - 888q^{54} - 2160q^{55} - 1246q^{56} - 2108q^{57} - 2948q^{58} - 1400q^{59} - 2656q^{60} - 164q^{61} - 486q^{63} - 152q^{64} - 36q^{65} - 126q^{66} - 292q^{67} - 72q^{68} - 222q^{69} - 100q^{70} - 240q^{71} + 664q^{72} + 112q^{73} + 568q^{74} + 2082q^{75} + 3796q^{76} + 1088q^{77} + 4022q^{78} + 1700q^{79} + 4260q^{80} + 3740q^{81} + 2072q^{82} + 1408q^{83} + 1875q^{84} + 2756q^{85} + 1780q^{86} + 988q^{87} + 1720q^{88} + 648q^{89} + 550q^{90} + 208q^{91} - 312q^{92} - 88q^{93} - 804q^{94} + 304q^{95} + 606q^{96} + 1324q^{97} + 1794q^{98} - 698q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(483))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
483.3.b \(\chi_{483}(323, \cdot)\) 483.3.b.a 88 1
483.3.c \(\chi_{483}(482, \cdot)\) n/a 124 1
483.3.f \(\chi_{483}(22, \cdot)\) 483.3.f.a 48 1
483.3.g \(\chi_{483}(139, \cdot)\) 483.3.g.a 60 1
483.3.k \(\chi_{483}(208, \cdot)\) n/a 116 2
483.3.l \(\chi_{483}(298, \cdot)\) n/a 128 2
483.3.o \(\chi_{483}(68, \cdot)\) n/a 248 2
483.3.p \(\chi_{483}(116, \cdot)\) n/a 236 2
483.3.s \(\chi_{483}(13, \cdot)\) n/a 640 10
483.3.t \(\chi_{483}(43, \cdot)\) n/a 480 10
483.3.w \(\chi_{483}(20, \cdot)\) n/a 1240 10
483.3.x \(\chi_{483}(8, \cdot)\) n/a 960 10
483.3.z \(\chi_{483}(2, \cdot)\) n/a 2480 20
483.3.ba \(\chi_{483}(5, \cdot)\) n/a 2480 20
483.3.bd \(\chi_{483}(37, \cdot)\) n/a 1280 20
483.3.be \(\chi_{483}(31, \cdot)\) n/a 1280 20

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(483))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(483)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)