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Properties

Label 845.4
Level 845
Weight 4
Dimension 76543
Nonzero newspaces 24
Sturm bound 227136
Trace bound 4

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Defining parameters

Level: \( N \) = \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(227136\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(845))\).

Total New Old
Modular forms 86088 77769 8319
Cusp forms 84264 76543 7721
Eisenstein series 1824 1226 598

Trace form

\( 76543 q - 136 q^{2} - 130 q^{3} - 124 q^{4} - 203 q^{5} - 404 q^{6} - 270 q^{7} - 420 q^{8} - 155 q^{9} + O(q^{10}) \) \( 76543 q - 136 q^{2} - 130 q^{3} - 124 q^{4} - 203 q^{5} - 404 q^{6} - 270 q^{7} - 420 q^{8} - 155 q^{9} + 2 q^{10} - 124 q^{11} + 820 q^{12} + 144 q^{13} + 204 q^{14} - 64 q^{15} - 460 q^{16} - 862 q^{17} - 3352 q^{18} - 1808 q^{19} - 1270 q^{20} - 384 q^{21} + 1300 q^{22} + 702 q^{23} + 4092 q^{24} - 185 q^{25} + 1068 q^{26} + 2960 q^{27} - 300 q^{28} - 1898 q^{29} - 1310 q^{30} - 1752 q^{31} - 2492 q^{32} - 2468 q^{33} - 3020 q^{34} - 228 q^{35} - 1204 q^{36} + 866 q^{37} + 4916 q^{38} - 810 q^{40} - 2258 q^{41} - 2700 q^{42} - 1370 q^{43} + 1060 q^{44} + 487 q^{45} + 3228 q^{46} - 118 q^{47} + 1276 q^{48} + 3449 q^{49} + 3014 q^{50} + 9424 q^{51} + 6924 q^{52} + 10070 q^{53} + 16420 q^{54} + 6194 q^{55} + 5916 q^{56} + 2804 q^{57} - 580 q^{58} - 2560 q^{59} - 23306 q^{60} - 10430 q^{61} - 26868 q^{62} - 33822 q^{63} - 42380 q^{64} - 10419 q^{65} - 41380 q^{66} - 14790 q^{67} - 13340 q^{68} - 6960 q^{69} - 5898 q^{70} + 5680 q^{71} + 7044 q^{72} + 8782 q^{73} + 14716 q^{74} + 15128 q^{75} + 12644 q^{76} + 14820 q^{77} + 22740 q^{78} + 10524 q^{79} + 36470 q^{80} + 21841 q^{81} + 19820 q^{82} + 13878 q^{83} + 19428 q^{84} + 1706 q^{85} - 13372 q^{86} - 15832 q^{87} - 1884 q^{88} - 15162 q^{89} - 14518 q^{90} - 5880 q^{91} - 20076 q^{92} - 17100 q^{93} - 4940 q^{94} - 4610 q^{95} + 6332 q^{96} + 7502 q^{97} - 9800 q^{98} + 19916 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(845))\)

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
845.4.a \(\chi_{845}(1, \cdot)\) 845.4.a.a 1 1
845.4.a.b 1
845.4.a.c 2
845.4.a.d 2
845.4.a.e 2
845.4.a.f 5
845.4.a.g 7
845.4.a.h 7
845.4.a.i 7
845.4.a.j 7
845.4.a.k 7
845.4.a.l 7
845.4.a.m 14
845.4.a.n 14
845.4.a.o 15
845.4.a.p 15
845.4.a.q 21
845.4.a.r 21
845.4.b \(\chi_{845}(339, \cdot)\) n/a 222 1
845.4.c \(\chi_{845}(506, \cdot)\) n/a 154 1
845.4.d \(\chi_{845}(844, \cdot)\) n/a 220 1
845.4.e \(\chi_{845}(146, \cdot)\) n/a 308 2
845.4.f \(\chi_{845}(408, \cdot)\) n/a 442 2
845.4.k \(\chi_{845}(268, \cdot)\) n/a 442 2
845.4.l \(\chi_{845}(654, \cdot)\) n/a 440 2
845.4.m \(\chi_{845}(316, \cdot)\) n/a 308 2
845.4.n \(\chi_{845}(484, \cdot)\) n/a 444 2
845.4.o \(\chi_{845}(258, \cdot)\) n/a 884 4
845.4.t \(\chi_{845}(188, \cdot)\) n/a 884 4
845.4.u \(\chi_{845}(66, \cdot)\) n/a 2184 12
845.4.v \(\chi_{845}(64, \cdot)\) n/a 3264 12
845.4.w \(\chi_{845}(51, \cdot)\) n/a 2184 12
845.4.x \(\chi_{845}(14, \cdot)\) n/a 3240 12
845.4.y \(\chi_{845}(16, \cdot)\) n/a 4368 24
845.4.z \(\chi_{845}(8, \cdot)\) n/a 6504 24
845.4.be \(\chi_{845}(18, \cdot)\) n/a 6504 24
845.4.bf \(\chi_{845}(9, \cdot)\) n/a 6480 24
845.4.bg \(\chi_{845}(36, \cdot)\) n/a 4368 24
845.4.bh \(\chi_{845}(4, \cdot)\) n/a 6528 24
845.4.bi \(\chi_{845}(7, \cdot)\) n/a 13008 48
845.4.bn \(\chi_{845}(2, \cdot)\) n/a 13008 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(845))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(845)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)