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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

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

Display 100 coefficients 10 coefficients

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 available 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

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