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Properties

Label 867.6
Level 867
Weight 6
Dimension 102953
Nonzero newspaces 10
Sturm bound 332928
Trace bound 2

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Defining parameters

Level: \( N \) = \( 867 = 3 \cdot 17^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(332928\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(867))\).

Total New Old
Modular forms 139520 103689 35831
Cusp forms 137920 102953 34967
Eisenstein series 1600 736 864

Trace form

\( 102953 q - 6 q^{2} - 111 q^{3} - 236 q^{4} + 6 q^{5} - 174 q^{6} - 280 q^{7} + 168 q^{8} - 39 q^{9} + O(q^{10}) \) \( 102953 q - 6 q^{2} - 111 q^{3} - 236 q^{4} + 6 q^{5} - 174 q^{6} - 280 q^{7} + 168 q^{8} - 39 q^{9} - 5332 q^{10} + 1964 q^{11} + 8364 q^{12} + 3630 q^{13} - 2576 q^{14} - 8754 q^{15} - 30080 q^{16} - 3824 q^{17} - 8654 q^{18} + 1476 q^{19} + 34072 q^{20} + 23952 q^{21} + 41288 q^{22} + 13592 q^{23} - 43440 q^{24} - 32561 q^{25} + 45516 q^{26} + 609 q^{27} + 132272 q^{28} + 28238 q^{29} - 22332 q^{30} - 73280 q^{31} - 147200 q^{32} - 74908 q^{33} - 135296 q^{34} - 105328 q^{35} - 13268 q^{36} + 16678 q^{37} + 128296 q^{38} + 159062 q^{39} + 481792 q^{40} + 160730 q^{41} - 28968 q^{42} + 110300 q^{43} - 79696 q^{44} - 99170 q^{45} - 465920 q^{46} - 18672 q^{47} + 264808 q^{48} - 15447 q^{49} + 18534 q^{50} + 78240 q^{51} + 2088 q^{52} - 449178 q^{53} - 267454 q^{54} - 3752 q^{55} + 401440 q^{56} + 207868 q^{57} + 905788 q^{58} + 462044 q^{59} + 23248 q^{60} + 341150 q^{61} + 14144 q^{62} - 205680 q^{63} - 475504 q^{64} - 826812 q^{65} - 526960 q^{66} - 597932 q^{67} - 1208560 q^{68} - 1047952 q^{69} - 1363824 q^{70} - 92760 q^{71} + 193632 q^{72} + 1305450 q^{73} + 1558908 q^{74} + 1256943 q^{75} + 2579200 q^{76} + 1781984 q^{77} + 1677572 q^{78} + 816560 q^{79} + 346240 q^{80} + 303353 q^{81} - 1844492 q^{82} - 1666252 q^{83} - 1356328 q^{84} - 1379416 q^{85} - 874504 q^{86} - 963690 q^{87} - 1544976 q^{88} - 273702 q^{89} - 2430812 q^{90} + 491680 q^{91} + 1629920 q^{92} - 141832 q^{93} + 2508976 q^{94} + 1381496 q^{95} + 2165848 q^{96} + 1483954 q^{97} + 1474218 q^{98} + 348580 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(867))\)

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
867.6.a \(\chi_{867}(1, \cdot)\) 867.6.a.a 1 1
867.6.a.b 1
867.6.a.c 1
867.6.a.d 2
867.6.a.e 3
867.6.a.f 4
867.6.a.g 5
867.6.a.h 5
867.6.a.i 5
867.6.a.j 8
867.6.a.k 8
867.6.a.l 8
867.6.a.m 8
867.6.a.n 16
867.6.a.o 16
867.6.a.p 18
867.6.a.q 18
867.6.a.r 21
867.6.a.s 21
867.6.a.t 28
867.6.a.u 28
867.6.d \(\chi_{867}(577, \cdot)\) n/a 224 1
867.6.e \(\chi_{867}(616, \cdot)\) n/a 448 2
867.6.h \(\chi_{867}(688, \cdot)\) n/a 904 4
867.6.i \(\chi_{867}(65, \cdot)\) n/a 3488 8
867.6.k \(\chi_{867}(52, \cdot)\) n/a 4096 16
867.6.l \(\chi_{867}(16, \cdot)\) n/a 4096 16
867.6.p \(\chi_{867}(4, \cdot)\) n/a 8192 32
867.6.q \(\chi_{867}(19, \cdot)\) n/a 16256 64
867.6.t \(\chi_{867}(5, \cdot)\) n/a 65024 128

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(867))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(867)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 1}\)