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Properties

Label 361.4
Level 361
Weight 4
Dimension 15921
Nonzero newspaces 6
Sturm bound 43320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 361 = 19^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(43320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(361))\).

Total New Old
Modular forms 16497 16390 107
Cusp forms 15993 15921 72
Eisenstein series 504 469 35

Trace form

\( 15921 q - 153 q^{2} - 153 q^{3} - 153 q^{4} - 153 q^{5} - 153 q^{6} - 153 q^{7} - 153 q^{8} - 153 q^{9} + O(q^{10}) \) \( 15921 q - 153 q^{2} - 153 q^{3} - 153 q^{4} - 153 q^{5} - 153 q^{6} - 153 q^{7} - 153 q^{8} - 153 q^{9} - 153 q^{10} - 153 q^{11} + 423 q^{12} + 135 q^{13} - 81 q^{14} - 369 q^{15} - 1017 q^{16} - 441 q^{17} - 1107 q^{18} - 540 q^{19} - 1449 q^{20} - 657 q^{21} - 477 q^{22} - 117 q^{23} + 711 q^{24} + 711 q^{25} + 1215 q^{26} + 2457 q^{27} + 4437 q^{28} + 1107 q^{29} + 2241 q^{30} + 27 q^{31} - 783 q^{32} - 1989 q^{33} - 2403 q^{34} - 2385 q^{35} - 6309 q^{36} - 1467 q^{37} - 2493 q^{38} - 4077 q^{39} - 3915 q^{40} - 1053 q^{41} - 3213 q^{42} + 99 q^{43} + 5697 q^{44} + 6003 q^{45} + 6885 q^{46} + 3591 q^{47} + 11061 q^{48} + 3267 q^{49} + 4257 q^{50} + 117 q^{51} - 4905 q^{52} - 3321 q^{53} - 5067 q^{54} - 4041 q^{55} - 12231 q^{56} - 2682 q^{57} - 4185 q^{58} - 4653 q^{59} - 3231 q^{60} + 5355 q^{61} + 6669 q^{62} + 6615 q^{63} + 8055 q^{64} + 5067 q^{65} + 6903 q^{66} + 1683 q^{67} + 7029 q^{68} + 495 q^{69} - 801 q^{70} + 4203 q^{71} - 6075 q^{72} - 10035 q^{73} - 10521 q^{74} - 12735 q^{75} - 6912 q^{76} - 9621 q^{77} + 387 q^{78} - 5481 q^{79} + 5607 q^{80} - 1107 q^{81} - 4599 q^{82} + 531 q^{83} + 2655 q^{84} + 1719 q^{85} + 2673 q^{86} + 2583 q^{87} + 2151 q^{88} + 7947 q^{89} + 8217 q^{90} + 9783 q^{91} + 4905 q^{92} + 459 q^{93} + 5553 q^{94} + 5544 q^{95} + 999 q^{96} + 6543 q^{97} + 13185 q^{98} + 1413 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(361))\)

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
361.4.a \(\chi_{361}(1, \cdot)\) 361.4.a.a 1 1
361.4.a.b 1
361.4.a.c 2
361.4.a.d 2
361.4.a.e 2
361.4.a.f 2
361.4.a.g 2
361.4.a.h 2
361.4.a.i 3
361.4.a.j 4
361.4.a.k 6
361.4.a.l 6
361.4.a.m 12
361.4.a.n 12
361.4.a.o 20
361.4.c \(\chi_{361}(68, \cdot)\) n/a 154 2
361.4.e \(\chi_{361}(28, \cdot)\) n/a 462 6
361.4.g \(\chi_{361}(20, \cdot)\) n/a 1692 18
361.4.i \(\chi_{361}(7, \cdot)\) n/a 3384 36
361.4.k \(\chi_{361}(4, \cdot)\) n/a 10152 108

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(361))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(361)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)