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Properties

Label 832.6
Level 832
Weight 6
Dimension 59518
Nonzero newspaces 28
Sturm bound 258048
Trace bound 17

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Defining parameters

Level: \( N \) = \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(258048\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(832))\).

Total New Old
Modular forms 108384 60002 48382
Cusp forms 106656 59518 47138
Eisenstein series 1728 484 1244

Trace form

\( 59518 q - 80 q^{2} - 60 q^{3} - 80 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 80 q^{8} + 386 q^{9} + O(q^{10}) \) \( 59518 q - 80 q^{2} - 60 q^{3} - 80 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 80 q^{8} + 386 q^{9} - 80 q^{10} - 1268 q^{11} - 80 q^{12} + 144 q^{13} - 176 q^{14} + 3536 q^{15} - 80 q^{16} + 1476 q^{17} - 80 q^{18} - 4780 q^{19} - 80 q^{20} - 10520 q^{21} - 27264 q^{22} - 56 q^{23} + 44000 q^{24} + 31078 q^{25} + 25872 q^{26} + 8304 q^{27} - 8800 q^{28} - 16368 q^{29} - 129840 q^{30} - 23144 q^{31} - 74400 q^{32} - 44464 q^{33} - 25600 q^{34} + 17216 q^{35} + 124560 q^{36} + 46816 q^{37} + 139200 q^{38} - 64 q^{39} + 124544 q^{40} - 26724 q^{41} - 92800 q^{42} - 30820 q^{43} - 131104 q^{44} + 46968 q^{45} - 80 q^{46} + 88296 q^{47} - 80 q^{48} + 24774 q^{49} + 274048 q^{50} - 89072 q^{51} - 73576 q^{52} - 77888 q^{53} - 466640 q^{54} + 440136 q^{55} - 301920 q^{56} - 70808 q^{57} - 52064 q^{58} - 175364 q^{59} + 395632 q^{60} + 100224 q^{61} + 350672 q^{62} - 659392 q^{63} + 749680 q^{64} - 14000 q^{65} + 509072 q^{66} - 395116 q^{67} + 14224 q^{68} - 287096 q^{69} - 573968 q^{70} + 575304 q^{71} - 828224 q^{72} + 169884 q^{73} - 755520 q^{74} + 1082388 q^{75} - 537040 q^{76} + 106472 q^{77} - 332752 q^{78} - 816576 q^{79} + 599648 q^{80} + 411118 q^{81} + 1006160 q^{82} + 455620 q^{83} + 1970000 q^{84} + 497888 q^{85} + 1443648 q^{86} - 56 q^{87} + 446480 q^{88} - 230468 q^{89} - 568880 q^{90} - 231228 q^{91} - 1842720 q^{92} - 722720 q^{93} - 1642640 q^{94} - 500832 q^{95} - 2428768 q^{96} - 1030604 q^{97} - 1914688 q^{98} - 597484 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(832))\)

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
832.6.a \(\chi_{832}(1, \cdot)\) 832.6.a.a 1 1
832.6.a.b 1
832.6.a.c 1
832.6.a.d 1
832.6.a.e 1
832.6.a.f 1
832.6.a.g 1
832.6.a.h 1
832.6.a.i 2
832.6.a.j 2
832.6.a.k 2
832.6.a.l 2
832.6.a.m 2
832.6.a.n 2
832.6.a.o 2
832.6.a.p 2
832.6.a.q 3
832.6.a.r 3
832.6.a.s 3
832.6.a.t 3
832.6.a.u 3
832.6.a.v 3
832.6.a.w 4
832.6.a.x 4
832.6.a.y 5
832.6.a.z 5
832.6.a.ba 6
832.6.a.bb 6
832.6.a.bc 7
832.6.a.bd 7
832.6.a.be 8
832.6.a.bf 8
832.6.a.bg 8
832.6.a.bh 10
832.6.b \(\chi_{832}(417, \cdot)\) n/a 120 1
832.6.e \(\chi_{832}(545, \cdot)\) n/a 140 1
832.6.f \(\chi_{832}(129, \cdot)\) n/a 138 1
832.6.i \(\chi_{832}(321, \cdot)\) n/a 276 2
832.6.k \(\chi_{832}(255, \cdot)\) n/a 276 2
832.6.l \(\chi_{832}(239, \cdot)\) n/a 276 2
832.6.n \(\chi_{832}(209, \cdot)\) n/a 240 2
832.6.p \(\chi_{832}(337, \cdot)\) n/a 276 2
832.6.s \(\chi_{832}(47, \cdot)\) n/a 276 2
832.6.u \(\chi_{832}(31, \cdot)\) n/a 280 2
832.6.w \(\chi_{832}(257, \cdot)\) n/a 276 2
832.6.z \(\chi_{832}(289, \cdot)\) n/a 280 2
832.6.ba \(\chi_{832}(225, \cdot)\) n/a 280 2
832.6.bd \(\chi_{832}(343, \cdot)\) None 0 4
832.6.bf \(\chi_{832}(105, \cdot)\) None 0 4
832.6.bg \(\chi_{832}(25, \cdot)\) None 0 4
832.6.bi \(\chi_{832}(135, \cdot)\) None 0 4
832.6.bk \(\chi_{832}(223, \cdot)\) n/a 560 4
832.6.bn \(\chi_{832}(175, \cdot)\) n/a 552 4
832.6.bp \(\chi_{832}(17, \cdot)\) n/a 552 4
832.6.br \(\chi_{832}(81, \cdot)\) n/a 552 4
832.6.bs \(\chi_{832}(15, \cdot)\) n/a 552 4
832.6.bu \(\chi_{832}(63, \cdot)\) n/a 552 4
832.6.bw \(\chi_{832}(99, \cdot)\) n/a 4464 8
832.6.by \(\chi_{832}(53, \cdot)\) n/a 3840 8
832.6.cb \(\chi_{832}(77, \cdot)\) n/a 4464 8
832.6.cc \(\chi_{832}(83, \cdot)\) n/a 4464 8
832.6.cf \(\chi_{832}(71, \cdot)\) None 0 8
832.6.ch \(\chi_{832}(121, \cdot)\) None 0 8
832.6.ci \(\chi_{832}(9, \cdot)\) None 0 8
832.6.ck \(\chi_{832}(7, \cdot)\) None 0 8
832.6.cn \(\chi_{832}(11, \cdot)\) n/a 8928 16
832.6.cp \(\chi_{832}(29, \cdot)\) n/a 8928 16
832.6.cq \(\chi_{832}(69, \cdot)\) n/a 8928 16
832.6.ct \(\chi_{832}(115, \cdot)\) n/a 8928 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(832))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(832)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 1}\)