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Properties

Label 882.6
Level 882
Weight 6
Dimension 26803
Nonzero newspaces 20
Sturm bound 254016
Trace bound 9

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Defining parameters

Level: \( N \) = \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(254016\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(882))\).

Total New Old
Modular forms 106800 26803 79997
Cusp forms 104880 26803 78077
Eisenstein series 1920 0 1920

Trace form

\( 26803 q - 8 q^{2} + 9 q^{3} + 32 q^{4} - 174 q^{5} - 84 q^{6} - 232 q^{7} + 64 q^{8} + 579 q^{9} + O(q^{10}) \) \( 26803 q - 8 q^{2} + 9 q^{3} + 32 q^{4} - 174 q^{5} - 84 q^{6} - 232 q^{7} + 64 q^{8} + 579 q^{9} + 1992 q^{10} + 555 q^{11} - 384 q^{12} + 2280 q^{13} - 360 q^{14} - 10536 q^{15} - 3584 q^{16} - 2064 q^{17} + 8520 q^{18} + 25734 q^{19} + 13728 q^{20} + 13644 q^{21} + 12732 q^{22} - 6666 q^{23} - 7104 q^{24} - 56330 q^{25} - 40120 q^{26} - 42264 q^{27} + 2688 q^{28} + 27960 q^{29} + 38112 q^{30} + 94788 q^{31} - 2048 q^{32} - 55653 q^{33} - 37836 q^{34} - 79770 q^{35} - 7440 q^{36} + 108458 q^{37} - 10612 q^{38} + 46536 q^{39} - 51456 q^{40} + 173253 q^{41} + 110077 q^{43} + 31104 q^{44} + 19500 q^{45} + 120600 q^{46} - 71262 q^{47} + 3840 q^{48} + 302922 q^{49} - 77528 q^{50} - 55683 q^{51} - 80288 q^{52} + 522174 q^{53} + 366660 q^{54} - 289758 q^{55} - 126720 q^{56} + 166659 q^{57} - 165456 q^{58} - 392283 q^{59} - 374400 q^{60} + 544576 q^{61} - 328072 q^{62} - 635208 q^{63} - 28672 q^{64} - 380448 q^{65} - 197184 q^{66} + 242747 q^{67} + 181392 q^{68} + 709668 q^{69} - 135432 q^{70} + 60528 q^{71} - 59712 q^{72} - 809844 q^{73} + 275768 q^{74} + 498069 q^{75} - 71088 q^{76} - 221580 q^{77} - 883896 q^{78} + 1523900 q^{79} + 38400 q^{80} + 307527 q^{81} + 469392 q^{82} + 957504 q^{83} + 70176 q^{85} + 943796 q^{86} + 1220274 q^{87} + 251328 q^{88} - 673482 q^{89} - 959520 q^{90} - 1064194 q^{91} - 1085088 q^{92} - 2290620 q^{93} - 1865784 q^{94} - 2856888 q^{95} - 110592 q^{96} + 260385 q^{97} + 95520 q^{98} + 1144626 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(882))\)

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
882.6.a \(\chi_{882}(1, \cdot)\) 882.6.a.a 1 1
882.6.a.b 1
882.6.a.c 1
882.6.a.d 1
882.6.a.e 1
882.6.a.f 1
882.6.a.g 1
882.6.a.h 1
882.6.a.i 1
882.6.a.j 1
882.6.a.k 1
882.6.a.l 1
882.6.a.m 1
882.6.a.n 1
882.6.a.o 1
882.6.a.p 1
882.6.a.q 1
882.6.a.r 1
882.6.a.s 1
882.6.a.t 1
882.6.a.u 1
882.6.a.v 1
882.6.a.w 1
882.6.a.x 1
882.6.a.y 1
882.6.a.z 2
882.6.a.ba 2
882.6.a.bb 2
882.6.a.bc 2
882.6.a.bd 2
882.6.a.be 2
882.6.a.bf 2
882.6.a.bg 2
882.6.a.bh 2
882.6.a.bi 2
882.6.a.bj 2
882.6.a.bk 2
882.6.a.bl 2
882.6.a.bm 2
882.6.a.bn 2
882.6.a.bo 2
882.6.a.bp 2
882.6.a.bq 2
882.6.a.br 2
882.6.a.bs 2
882.6.a.bt 2
882.6.a.bu 2
882.6.a.bv 4
882.6.a.bw 6
882.6.a.bx 6
882.6.d \(\chi_{882}(881, \cdot)\) 882.6.d.a 16 1
882.6.d.b 24
882.6.d.c 24
882.6.e \(\chi_{882}(373, \cdot)\) n/a 400 2
882.6.f \(\chi_{882}(295, \cdot)\) n/a 410 2
882.6.g \(\chi_{882}(361, \cdot)\) n/a 168 2
882.6.h \(\chi_{882}(67, \cdot)\) n/a 400 2
882.6.k \(\chi_{882}(215, \cdot)\) n/a 136 2
882.6.l \(\chi_{882}(227, \cdot)\) n/a 400 2
882.6.m \(\chi_{882}(293, \cdot)\) n/a 400 2
882.6.t \(\chi_{882}(803, \cdot)\) n/a 400 2
882.6.u \(\chi_{882}(127, \cdot)\) n/a 708 6
882.6.v \(\chi_{882}(125, \cdot)\) n/a 576 6
882.6.y \(\chi_{882}(193, \cdot)\) n/a 3360 12
882.6.z \(\chi_{882}(37, \cdot)\) n/a 1392 12
882.6.ba \(\chi_{882}(43, \cdot)\) n/a 3360 12
882.6.bb \(\chi_{882}(25, \cdot)\) n/a 3360 12
882.6.bc \(\chi_{882}(47, \cdot)\) n/a 3360 12
882.6.bj \(\chi_{882}(41, \cdot)\) n/a 3360 12
882.6.bk \(\chi_{882}(5, \cdot)\) n/a 3360 12
882.6.bl \(\chi_{882}(17, \cdot)\) n/a 1104 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(882))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(882)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 1}\)