Properties

Label 845.6
Level 845
Weight 6
Dimension 127981
Nonzero newspaces 24
Sturm bound 340704
Trace bound 4

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Defining parameters

Level: \( N \) = \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(340704\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(845))\).

Total New Old
Modular forms 142872 129207 13665
Cusp forms 141048 127981 13067
Eisenstein series 1824 1226 598

Trace form

\( 127981 q - 130 q^{2} - 136 q^{3} - 184 q^{4} - 263 q^{5} - 140 q^{6} - 1132 q^{7} + 2052 q^{8} + 1927 q^{9} + O(q^{10}) \) \( 127981 q - 130 q^{2} - 136 q^{3} - 184 q^{4} - 263 q^{5} - 140 q^{6} - 1132 q^{7} + 2052 q^{8} + 1927 q^{9} - 468 q^{10} - 2176 q^{11} - 11564 q^{12} - 3288 q^{13} - 1188 q^{14} + 3398 q^{15} + 18212 q^{16} - 6598 q^{17} + 13166 q^{18} + 20440 q^{19} + 11174 q^{20} + 11124 q^{21} + 3052 q^{22} - 10068 q^{23} - 92100 q^{24} + 2265 q^{25} - 36372 q^{26} - 58996 q^{27} - 95644 q^{28} - 16742 q^{29} + 93994 q^{30} + 129948 q^{31} + 322084 q^{32} + 165748 q^{33} + 79104 q^{34} - 30498 q^{35} - 371728 q^{36} - 143906 q^{37} - 205972 q^{38} - 154128 q^{39} - 203842 q^{40} - 21074 q^{41} + 262788 q^{42} + 336488 q^{43} + 545524 q^{44} + 277747 q^{45} + 394940 q^{46} + 158588 q^{47} + 114556 q^{48} - 233773 q^{49} - 84880 q^{50} - 520556 q^{51} - 403148 q^{52} - 377494 q^{53} - 778700 q^{54} - 496246 q^{55} - 444228 q^{56} - 48316 q^{57} + 349928 q^{58} + 267656 q^{59} + 901174 q^{60} + 948170 q^{61} + 17628 q^{62} + 400164 q^{63} + 640308 q^{64} + 309459 q^{65} + 943580 q^{66} + 270344 q^{67} + 2003500 q^{68} + 752604 q^{69} + 72054 q^{70} + 185452 q^{71} - 1595796 q^{72} - 1064058 q^{73} - 2787752 q^{74} - 1990954 q^{75} - 2203916 q^{76} - 1166940 q^{77} - 1102332 q^{78} + 478852 q^{79} + 1196486 q^{80} + 968791 q^{81} + 1022672 q^{82} + 413136 q^{83} + 965796 q^{84} - 155142 q^{85} + 259868 q^{86} - 17500 q^{87} + 963588 q^{88} + 1619562 q^{89} + 1882088 q^{90} + 898348 q^{91} + 704772 q^{92} + 1629588 q^{93} - 1117932 q^{94} - 500546 q^{95} - 2496772 q^{96} - 909218 q^{97} - 2349218 q^{98} - 1511896 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(845))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
845.6.a \(\chi_{845}(1, \cdot)\) 845.6.a.a 1 1
845.6.a.b 1
845.6.a.c 3
845.6.a.d 4
845.6.a.e 4
845.6.a.f 4
845.6.a.g 6
845.6.a.h 6
845.6.a.i 7
845.6.a.j 7
845.6.a.k 12
845.6.a.l 12
845.6.a.m 12
845.6.a.n 12
845.6.a.o 24
845.6.a.p 24
845.6.a.q 27
845.6.a.r 27
845.6.a.s 33
845.6.a.t 33
845.6.b \(\chi_{845}(339, \cdot)\) n/a 376 1
845.6.c \(\chi_{845}(506, \cdot)\) n/a 258 1
845.6.d \(\chi_{845}(844, \cdot)\) n/a 376 1
845.6.e \(\chi_{845}(146, \cdot)\) n/a 512 2
845.6.f \(\chi_{845}(408, \cdot)\) n/a 750 2
845.6.k \(\chi_{845}(268, \cdot)\) n/a 750 2
845.6.l \(\chi_{845}(654, \cdot)\) n/a 752 2
845.6.m \(\chi_{845}(316, \cdot)\) n/a 512 2
845.6.n \(\chi_{845}(484, \cdot)\) n/a 748 2
845.6.o \(\chi_{845}(258, \cdot)\) n/a 1500 4
845.6.t \(\chi_{845}(188, \cdot)\) n/a 1500 4
845.6.u \(\chi_{845}(66, \cdot)\) n/a 3624 12
845.6.v \(\chi_{845}(64, \cdot)\) n/a 5424 12
845.6.w \(\chi_{845}(51, \cdot)\) n/a 3624 12
845.6.x \(\chi_{845}(14, \cdot)\) n/a 5448 12
845.6.y \(\chi_{845}(16, \cdot)\) n/a 7296 24
845.6.z \(\chi_{845}(8, \cdot)\) n/a 10872 24
845.6.be \(\chi_{845}(18, \cdot)\) n/a 10872 24
845.6.bf \(\chi_{845}(9, \cdot)\) n/a 10896 24
845.6.bg \(\chi_{845}(36, \cdot)\) n/a 7296 24
845.6.bh \(\chi_{845}(4, \cdot)\) n/a 10848 24
845.6.bi \(\chi_{845}(7, \cdot)\) n/a 21744 48
845.6.bn \(\chi_{845}(2, \cdot)\) n/a 21744 48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(845))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(845)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)