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Properties

Label 483.8
Level 483
Weight 8
Dimension 42132
Nonzero newspaces 16
Sturm bound 135168
Trace bound 3

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Defining parameters

Level: \( N \) = \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(135168\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(483))\).

Total New Old
Modular forms 59664 42548 17116
Cusp forms 58608 42132 16476
Eisenstein series 1056 416 640

Trace form

\( 42132 q + 24 q^{2} - 92 q^{3} - 1468 q^{4} + 1548 q^{5} + 1900 q^{6} + 1102 q^{7} - 12588 q^{8} + 5944 q^{9} + O(q^{10}) \) \( 42132 q + 24 q^{2} - 92 q^{3} - 1468 q^{4} + 1548 q^{5} + 1900 q^{6} + 1102 q^{7} - 12588 q^{8} + 5944 q^{9} - 27064 q^{10} + 1212 q^{11} + 52180 q^{12} - 4044 q^{13} + 77808 q^{14} - 81732 q^{15} + 335428 q^{16} - 51692 q^{17} - 590064 q^{18} - 232288 q^{19} + 770488 q^{20} + 267008 q^{21} - 27272 q^{22} + 452288 q^{23} + 512168 q^{24} - 281228 q^{25} - 219508 q^{26} - 1301834 q^{27} - 33858 q^{28} + 149668 q^{29} + 1940904 q^{30} - 950944 q^{31} + 966884 q^{32} - 3351726 q^{33} - 5418824 q^{34} + 5084032 q^{35} + 4767682 q^{36} + 7440912 q^{37} - 6209344 q^{38} - 8454200 q^{39} - 30940040 q^{40} - 8832496 q^{41} - 8545717 q^{42} + 5433972 q^{43} + 31716172 q^{44} + 10643442 q^{45} + 33521764 q^{46} + 7922836 q^{47} + 5306852 q^{48} - 13087606 q^{49} - 34481744 q^{50} - 27022220 q^{51} - 72369056 q^{52} - 7856224 q^{53} + 31023900 q^{54} + 19458792 q^{55} + 35919886 q^{56} + 29562868 q^{57} + 86338900 q^{58} + 851888 q^{59} - 7023184 q^{60} - 40009980 q^{61} - 59249160 q^{62} - 12277416 q^{63} - 39770344 q^{64} - 5449188 q^{65} - 12961266 q^{66} + 48013300 q^{67} + 34209600 q^{68} - 24321846 q^{69} + 63130628 q^{70} + 3141096 q^{71} - 4026344 q^{72} - 6377928 q^{73} - 121738208 q^{74} + 46758202 q^{75} + 107824588 q^{76} + 66524600 q^{77} + 182904222 q^{78} + 20360124 q^{79} - 98274588 q^{80} - 184206064 q^{81} - 116929408 q^{82} - 86001704 q^{83} - 168901217 q^{84} - 149407076 q^{85} - 152382068 q^{86} - 42907340 q^{87} + 69984112 q^{88} + 111340632 q^{89} + 308917094 q^{90} + 180250140 q^{91} + 299128644 q^{92} + 261829784 q^{93} + 243381556 q^{94} - 41055024 q^{95} - 9468614 q^{96} + 19758708 q^{97} + 227936410 q^{98} - 245588810 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(483))\)

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
483.8.a \(\chi_{483}(1, \cdot)\) 483.8.a.a 18 1
483.8.a.b 18
483.8.a.c 18
483.8.a.d 18
483.8.a.e 20
483.8.a.f 20
483.8.a.g 20
483.8.a.h 20
483.8.d \(\chi_{483}(461, \cdot)\) n/a 412 1
483.8.e \(\chi_{483}(344, \cdot)\) n/a 336 1
483.8.h \(\chi_{483}(160, \cdot)\) n/a 224 1
483.8.i \(\chi_{483}(277, \cdot)\) n/a 412 2
483.8.j \(\chi_{483}(229, \cdot)\) n/a 448 2
483.8.m \(\chi_{483}(137, \cdot)\) n/a 888 2
483.8.n \(\chi_{483}(47, \cdot)\) n/a 820 2
483.8.q \(\chi_{483}(64, \cdot)\) n/a 1680 10
483.8.r \(\chi_{483}(34, \cdot)\) n/a 2240 10
483.8.u \(\chi_{483}(113, \cdot)\) n/a 3360 10
483.8.v \(\chi_{483}(41, \cdot)\) n/a 4440 10
483.8.y \(\chi_{483}(4, \cdot)\) n/a 4480 20
483.8.bb \(\chi_{483}(26, \cdot)\) n/a 8880 20
483.8.bc \(\chi_{483}(11, \cdot)\) n/a 8880 20
483.8.bf \(\chi_{483}(10, \cdot)\) n/a 4480 20

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(483))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(483)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 1}\)