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Properties

Label 484.6
Level 484
Weight 6
Dimension 20686
Nonzero newspaces 8
Sturm bound 87120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 484 = 2^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(87120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(484))\).

Total New Old
Modular forms 36700 20966 15734
Cusp forms 35900 20686 15214
Eisenstein series 800 280 520

Trace form

\( 20686 q - 45 q^{2} - 12 q^{3} - 45 q^{4} - 36 q^{5} - 45 q^{6} - 678 q^{7} - 45 q^{8} + 911 q^{9} + O(q^{10}) \) \( 20686 q - 45 q^{2} - 12 q^{3} - 45 q^{4} - 36 q^{5} - 45 q^{6} - 678 q^{7} - 45 q^{8} + 911 q^{9} - 55 q^{10} + 445 q^{11} - 85 q^{12} - 1518 q^{13} - 5435 q^{14} - 4168 q^{15} + 12715 q^{16} + 7834 q^{17} + 4005 q^{18} - 3634 q^{19} - 17095 q^{20} - 16694 q^{21} - 12620 q^{22} + 5526 q^{23} - 585 q^{24} - 519 q^{25} + 32405 q^{26} + 10704 q^{27} + 46505 q^{28} + 16106 q^{29} - 4455 q^{30} - 11584 q^{31} - 55 q^{32} + 6840 q^{33} - 21885 q^{34} + 41278 q^{35} - 130075 q^{36} + 90472 q^{37} - 39095 q^{38} - 45514 q^{39} + 42025 q^{40} - 106794 q^{41} + 179925 q^{42} - 13840 q^{43} + 63125 q^{44} - 208416 q^{45} + 66485 q^{46} - 74446 q^{47} - 73855 q^{48} + 54097 q^{49} - 202725 q^{50} + 58582 q^{51} - 364635 q^{52} + 320254 q^{53} - 55 q^{54} + 126710 q^{55} + 523215 q^{56} + 104968 q^{57} + 369225 q^{58} + 94412 q^{59} + 69705 q^{60} - 58878 q^{61} - 337695 q^{62} - 470888 q^{63} - 468645 q^{64} - 644422 q^{65} - 270385 q^{66} - 406458 q^{67} - 373015 q^{68} - 64932 q^{69} + 135025 q^{70} + 73248 q^{71} + 810255 q^{72} + 370702 q^{73} + 658205 q^{74} + 915838 q^{75} - 55 q^{76} + 277635 q^{77} - 267065 q^{78} + 120558 q^{79} - 567535 q^{80} + 38409 q^{81} - 646185 q^{82} - 286834 q^{83} + 405925 q^{84} - 359384 q^{85} + 571395 q^{86} - 929972 q^{87} + 598430 q^{88} - 363106 q^{89} + 329945 q^{90} - 696586 q^{91} - 446215 q^{92} + 240338 q^{93} - 30535 q^{94} + 1269794 q^{95} + 772585 q^{96} + 748272 q^{97} - 55 q^{98} + 875150 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(484))\)

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
484.6.a \(\chi_{484}(1, \cdot)\) 484.6.a.a 1 1
484.6.a.b 1
484.6.a.c 2
484.6.a.d 2
484.6.a.e 2
484.6.a.f 4
484.6.a.g 4
484.6.a.h 10
484.6.a.i 10
484.6.a.j 10
484.6.c \(\chi_{484}(483, \cdot)\) n/a 262 1
484.6.e \(\chi_{484}(9, \cdot)\) n/a 180 4
484.6.g \(\chi_{484}(215, \cdot)\) n/a 1048 4
484.6.i \(\chi_{484}(45, \cdot)\) n/a 550 10
484.6.j \(\chi_{484}(43, \cdot)\) n/a 3280 10
484.6.m \(\chi_{484}(5, \cdot)\) n/a 2200 40
484.6.p \(\chi_{484}(7, \cdot)\) n/a 13120 40

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(484))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(484)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)