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Properties

Label 484.4
Level 484
Weight 4
Dimension 12355
Nonzero newspaces 8
Sturm bound 58080
Trace bound 1

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Defining parameters

Level: \( N \) = \( 484 = 2^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(58080\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(484))\).

Total New Old
Modular forms 22180 12635 9545
Cusp forms 21380 12355 9025
Eisenstein series 800 280 520

Trace form

\( 12355 q - 45 q^{2} - 45 q^{4} - 90 q^{5} - 45 q^{6} + 20 q^{7} - 45 q^{8} - 250 q^{9} + O(q^{10}) \) \( 12355 q - 45 q^{2} - 45 q^{4} - 90 q^{5} - 45 q^{6} + 20 q^{7} - 45 q^{8} - 250 q^{9} - 55 q^{10} - 50 q^{11} - 85 q^{12} - 130 q^{13} - 395 q^{14} - 220 q^{15} - 405 q^{16} + 250 q^{17} + 405 q^{18} + 450 q^{19} + 905 q^{20} + 730 q^{21} + 580 q^{22} + 960 q^{23} + 855 q^{24} + 750 q^{25} + 5 q^{26} - 330 q^{27} - 1095 q^{28} - 1390 q^{29} - 1815 q^{30} - 1980 q^{31} - 55 q^{32} - 1905 q^{33} + 1795 q^{34} - 1880 q^{35} + 725 q^{36} - 250 q^{37} - 695 q^{38} + 1220 q^{39} - 2215 q^{40} + 3330 q^{41} - 4635 q^{42} + 3980 q^{43} - 1555 q^{44} + 7890 q^{45} - 2715 q^{46} + 680 q^{47} - 2575 q^{48} - 510 q^{49} - 1365 q^{50} - 3650 q^{51} - 3275 q^{52} - 9050 q^{53} - 55 q^{54} - 2870 q^{55} + 1935 q^{56} - 6740 q^{57} + 2345 q^{58} + 590 q^{59} + 6105 q^{60} + 2870 q^{61} + 7905 q^{62} + 8800 q^{63} + 7515 q^{64} + 8450 q^{65} + 4175 q^{66} + 8380 q^{67} + 7625 q^{68} + 5730 q^{69} + 8785 q^{70} + 960 q^{71} + 11055 q^{72} + 810 q^{73} + 3725 q^{74} - 7670 q^{75} - 55 q^{76} - 3690 q^{77} - 8825 q^{78} - 6780 q^{79} - 15055 q^{80} - 8760 q^{81} - 14025 q^{82} + 830 q^{83} - 13115 q^{84} + 710 q^{85} - 6765 q^{86} + 3400 q^{87} - 7010 q^{88} - 670 q^{89} - 20215 q^{90} - 3160 q^{91} - 15895 q^{92} - 9670 q^{93} - 14615 q^{94} - 8260 q^{95} - 11495 q^{96} - 7620 q^{97} - 55 q^{98} - 3970 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(484))\)

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
484.4.a \(\chi_{484}(1, \cdot)\) 484.4.a.a 1 1
484.4.a.b 2
484.4.a.c 2
484.4.a.d 2
484.4.a.e 2
484.4.a.f 3
484.4.a.g 3
484.4.a.h 6
484.4.a.i 6
484.4.c \(\chi_{484}(483, \cdot)\) n/a 154 1
484.4.e \(\chi_{484}(9, \cdot)\) n/a 108 4
484.4.g \(\chi_{484}(215, \cdot)\) n/a 616 4
484.4.i \(\chi_{484}(45, \cdot)\) n/a 330 10
484.4.j \(\chi_{484}(43, \cdot)\) n/a 1960 10
484.4.m \(\chi_{484}(5, \cdot)\) n/a 1320 40
484.4.p \(\chi_{484}(7, \cdot)\) n/a 7840 40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(484))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(484)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 1}\)