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Properties

Label 882.5
Level 882
Weight 5
Dimension 21440
Nonzero newspaces 20
Sturm bound 211680
Trace bound 9

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Defining parameters

Level: \( N \) = \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(211680\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(882))\).

Total New Old
Modular forms 85632 21440 64192
Cusp forms 83712 21440 62272
Eisenstein series 1920 0 1920

Trace form

\( 21440 q + 6 q^{3} - 90 q^{5} + 48 q^{6} + 104 q^{7} - 78 q^{9} + O(q^{10}) \) \( 21440 q + 6 q^{3} - 90 q^{5} + 48 q^{6} + 104 q^{7} - 78 q^{9} + 192 q^{10} - 1332 q^{11} - 144 q^{12} - 2566 q^{13} - 864 q^{14} + 2334 q^{15} + 512 q^{16} + 8964 q^{17} + 2688 q^{18} + 4184 q^{19} + 144 q^{20} - 1476 q^{21} - 5424 q^{22} - 12150 q^{23} - 2688 q^{24} - 7462 q^{25} - 5760 q^{26} - 3816 q^{27} - 336 q^{28} + 9090 q^{29} + 6144 q^{30} - 8242 q^{31} - 2616 q^{33} - 96 q^{34} + 12546 q^{35} + 1056 q^{36} + 1972 q^{37} + 5328 q^{38} + 15930 q^{39} + 3840 q^{40} + 19368 q^{41} - 2256 q^{43} + 7200 q^{44} - 25014 q^{45} + 10464 q^{46} - 41490 q^{47} - 1536 q^{48} - 37068 q^{49} + 15552 q^{50} + 16650 q^{51} - 2640 q^{52} - 34416 q^{53} - 43632 q^{54} + 5118 q^{55} - 13824 q^{56} - 74538 q^{57} + 16800 q^{58} - 52092 q^{59} - 26928 q^{60} + 62292 q^{61} + 42336 q^{62} + 21000 q^{63} - 12288 q^{64} + 52542 q^{65} + 69216 q^{66} - 111788 q^{67} + 46800 q^{68} + 124038 q^{69} - 33120 q^{70} + 55872 q^{71} + 5376 q^{72} + 36224 q^{73} + 34272 q^{74} + 6846 q^{75} + 25040 q^{76} - 12798 q^{77} - 129504 q^{78} + 119506 q^{79} + 6912 q^{80} - 13566 q^{81} - 18816 q^{82} - 39114 q^{83} - 75540 q^{85} - 100080 q^{86} - 176094 q^{87} - 44160 q^{88} - 108540 q^{89} - 18912 q^{90} + 28688 q^{91} + 53424 q^{92} + 67914 q^{93} + 139296 q^{94} + 289044 q^{95} + 24576 q^{96} + 324104 q^{97} + 116352 q^{98} + 188286 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(882))\)

We only show spaces with odd 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
882.5.b \(\chi_{882}(197, \cdot)\) 882.5.b.a 4 1
882.5.b.b 4
882.5.b.c 4
882.5.b.d 4
882.5.b.e 6
882.5.b.f 6
882.5.b.g 6
882.5.b.h 6
882.5.b.i 8
882.5.b.j 8
882.5.c \(\chi_{882}(685, \cdot)\) 882.5.c.a 4 1
882.5.c.b 4
882.5.c.c 4
882.5.c.d 4
882.5.c.e 8
882.5.c.f 8
882.5.c.g 8
882.5.c.h 8
882.5.c.i 8
882.5.c.j 12
882.5.i \(\chi_{882}(569, \cdot)\) n/a 320 2
882.5.j \(\chi_{882}(31, \cdot)\) n/a 320 2
882.5.n \(\chi_{882}(19, \cdot)\) n/a 132 2
882.5.o \(\chi_{882}(97, \cdot)\) n/a 320 2
882.5.p \(\chi_{882}(607, \cdot)\) n/a 320 2
882.5.q \(\chi_{882}(491, \cdot)\) n/a 328 2
882.5.r \(\chi_{882}(263, \cdot)\) n/a 320 2
882.5.s \(\chi_{882}(557, \cdot)\) n/a 104 2
882.5.w \(\chi_{882}(55, \cdot)\) n/a 552 6
882.5.x \(\chi_{882}(71, \cdot)\) n/a 432 6
882.5.bd \(\chi_{882}(53, \cdot)\) n/a 912 12
882.5.be \(\chi_{882}(11, \cdot)\) n/a 2688 12
882.5.bf \(\chi_{882}(29, \cdot)\) n/a 2688 12
882.5.bg \(\chi_{882}(103, \cdot)\) n/a 2688 12
882.5.bh \(\chi_{882}(13, \cdot)\) n/a 2688 12
882.5.bi \(\chi_{882}(73, \cdot)\) n/a 1128 12
882.5.bm \(\chi_{882}(61, \cdot)\) n/a 2688 12
882.5.bn \(\chi_{882}(65, \cdot)\) n/a 2688 12

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(882))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(882)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)