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Properties

Label 471.6
Level 471
Weight 6
Dimension 30652
Nonzero newspaces 12
Sturm bound 98592
Trace bound 2

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Defining parameters

Level: \( N \) = \( 471 = 3 \cdot 157 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(98592\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(471))\).

Total New Old
Modular forms 41392 30964 10428
Cusp forms 40768 30652 10116
Eisenstein series 624 312 312

Trace form

\( 30652 q + 12 q^{2} - 96 q^{3} - 164 q^{4} - 12 q^{5} + 30 q^{6} - 76 q^{7} - 336 q^{8} - 240 q^{9} + O(q^{10}) \) \( 30652 q + 12 q^{2} - 96 q^{3} - 164 q^{4} - 12 q^{5} + 30 q^{6} - 76 q^{7} - 336 q^{8} - 240 q^{9} - 84 q^{10} + 1128 q^{11} - 150 q^{12} - 1432 q^{13} - 480 q^{14} - 186 q^{15} + 2116 q^{16} - 1764 q^{17} + 894 q^{18} + 956 q^{19} - 48 q^{20} + 642 q^{21} - 6924 q^{22} + 1680 q^{23} - 3102 q^{24} + 6022 q^{25} + 7656 q^{26} - 1536 q^{27} + 164 q^{28} - 9276 q^{29} + 570 q^{30} - 8956 q^{31} - 2880 q^{32} + 10074 q^{33} + 10428 q^{34} + 480 q^{35} - 726 q^{36} + 4664 q^{37} - 6672 q^{38} - 11562 q^{39} - 2172 q^{40} + 13740 q^{41} - 4398 q^{42} - 19444 q^{43} + 4512 q^{44} - 1050 q^{45} - 10236 q^{46} + 37344 q^{47} + 20370 q^{48} + 30258 q^{49} - 37068 q^{50} - 15954 q^{51} - 5260 q^{52} - 67500 q^{53} + 8670 q^{54} + 6612 q^{55} + 13440 q^{56} + 9930 q^{57} + 55500 q^{58} + 36168 q^{59} - 510 q^{60} - 79672 q^{61} + 52800 q^{62} + 6402 q^{63} - 55580 q^{64} - 7656 q^{65} - 60990 q^{66} + 45980 q^{67} - 7056 q^{68} + 15042 q^{69} - 3036 q^{70} + 8496 q^{71} - 27294 q^{72} + 82064 q^{73} - 28920 q^{74} + 55524 q^{75} + 4292 q^{76} - 45120 q^{77} + 68826 q^{78} - 43996 q^{79} + 13632 q^{80} - 13200 q^{81} - 82596 q^{82} - 164904 q^{83} + 2802 q^{84} - 10740 q^{85} + 115728 q^{86} - 83562 q^{87} + 189348 q^{88} + 188172 q^{89} + 5754 q^{90} + 50884 q^{91} + 6720 q^{92} - 79278 q^{93} - 224220 q^{94} + 6672 q^{95} - 25998 q^{96} - 99040 q^{97} - 182484 q^{98} + 91290 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(471))\)

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
471.6.a \(\chi_{471}(1, \cdot)\) 471.6.a.a 27 1
471.6.a.b 30
471.6.a.c 35
471.6.a.d 38
471.6.b \(\chi_{471}(313, \cdot)\) n/a 130 1
471.6.e \(\chi_{471}(169, \cdot)\) n/a 266 2
471.6.f \(\chi_{471}(185, \cdot)\) n/a 524 2
471.6.h \(\chi_{471}(13, \cdot)\) n/a 262 2
471.6.l \(\chi_{471}(50, \cdot)\) n/a 1044 4
471.6.m \(\chi_{471}(16, \cdot)\) n/a 1584 12
471.6.p \(\chi_{471}(4, \cdot)\) n/a 1560 12
471.6.q \(\chi_{471}(19, \cdot)\) n/a 3192 24
471.6.s \(\chi_{471}(2, \cdot)\) n/a 6288 24
471.6.v \(\chi_{471}(10, \cdot)\) n/a 3144 24
471.6.w \(\chi_{471}(5, \cdot)\) n/a 12528 48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(471))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(471)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(157))\)\(^{\oplus 2}\)