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Properties

Label 798.4
Level 798
Weight 4
Dimension 12352
Nonzero newspaces 32
Sturm bound 138240
Trace bound 18

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Defining parameters

Level: \( N \) = \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(138240\)
Trace bound: \(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(798))\).

Total New Old
Modular forms 52704 12352 40352
Cusp forms 50976 12352 38624
Eisenstein series 1728 0 1728

Trace form

\( 12352 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 72 q^{5} - 48 q^{6} - 224 q^{7} - 32 q^{8} + 120 q^{9} + O(q^{10}) \) \( 12352 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 72 q^{5} - 48 q^{6} - 224 q^{7} - 32 q^{8} + 120 q^{9} + 96 q^{10} + 216 q^{11} + 336 q^{12} + 1280 q^{13} + 136 q^{14} - 1008 q^{15} + 64 q^{16} - 1680 q^{17} + 264 q^{18} - 2600 q^{19} - 1056 q^{20} + 888 q^{21} - 744 q^{22} + 648 q^{23} + 192 q^{24} + 3940 q^{25} + 3344 q^{26} + 1746 q^{27} + 928 q^{28} + 2448 q^{29} - 1200 q^{30} - 1528 q^{31} - 128 q^{32} - 4608 q^{33} - 624 q^{34} - 4176 q^{35} - 1488 q^{36} - 472 q^{37} + 136 q^{38} - 2220 q^{39} + 384 q^{40} - 864 q^{41} + 456 q^{42} - 1408 q^{43} + 864 q^{44} - 2016 q^{45} - 2016 q^{46} + 4152 q^{47} - 672 q^{48} - 5240 q^{49} - 3704 q^{50} + 2502 q^{51} - 832 q^{52} - 1728 q^{53} + 5256 q^{54} + 3384 q^{55} + 448 q^{56} + 11808 q^{57} + 4800 q^{58} + 2304 q^{59} + 5904 q^{60} + 16448 q^{61} + 7136 q^{62} + 10554 q^{63} + 1792 q^{64} + 4776 q^{65} - 576 q^{66} + 1760 q^{67} - 2112 q^{68} - 16128 q^{69} - 1632 q^{70} - 8424 q^{71} - 4944 q^{72} - 18388 q^{73} - 1024 q^{74} - 15252 q^{75} - 272 q^{76} + 4836 q^{77} + 7488 q^{78} + 4328 q^{79} - 1152 q^{80} + 12744 q^{81} + 4656 q^{82} + 10824 q^{83} - 576 q^{84} + 672 q^{85} - 5104 q^{86} - 12024 q^{87} + 960 q^{88} - 8688 q^{89} - 15912 q^{90} - 7456 q^{91} - 14208 q^{92} - 27120 q^{93} - 30144 q^{94} - 24600 q^{95} + 768 q^{96} - 25168 q^{97} - 11720 q^{98} - 32598 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(798))\)

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
798.4.a \(\chi_{798}(1, \cdot)\) 798.4.a.a 1 1
798.4.a.b 1
798.4.a.c 1
798.4.a.d 2
798.4.a.e 3
798.4.a.f 3
798.4.a.g 3
798.4.a.h 3
798.4.a.i 3
798.4.a.j 3
798.4.a.k 4
798.4.a.l 4
798.4.a.m 4
798.4.a.n 4
798.4.a.o 4
798.4.a.p 4
798.4.a.q 4
798.4.a.r 5
798.4.b \(\chi_{798}(113, \cdot)\) n/a 120 1
798.4.e \(\chi_{798}(265, \cdot)\) 798.4.e.a 40 1
798.4.e.b 40
798.4.f \(\chi_{798}(419, \cdot)\) n/a 144 1
798.4.i \(\chi_{798}(163, \cdot)\) n/a 160 2
798.4.j \(\chi_{798}(457, \cdot)\) n/a 144 2
798.4.k \(\chi_{798}(463, \cdot)\) n/a 120 2
798.4.l \(\chi_{798}(121, \cdot)\) n/a 160 2
798.4.m \(\chi_{798}(145, \cdot)\) n/a 160 2
798.4.p \(\chi_{798}(107, \cdot)\) n/a 320 2
798.4.r \(\chi_{798}(83, \cdot)\) n/a 320 2
798.4.u \(\chi_{798}(647, \cdot)\) n/a 288 2
798.4.w \(\chi_{798}(311, \cdot)\) n/a 320 2
798.4.ba \(\chi_{798}(407, \cdot)\) n/a 240 2
798.4.bc \(\chi_{798}(31, \cdot)\) n/a 160 2
798.4.be \(\chi_{798}(493, \cdot)\) n/a 160 2
798.4.bf \(\chi_{798}(569, \cdot)\) n/a 320 2
798.4.bh \(\chi_{798}(65, \cdot)\) n/a 320 2
798.4.bj \(\chi_{798}(559, \cdot)\) n/a 160 2
798.4.bn \(\chi_{798}(353, \cdot)\) n/a 320 2
798.4.bo \(\chi_{798}(43, \cdot)\) n/a 360 6
798.4.bp \(\chi_{798}(289, \cdot)\) n/a 480 6
798.4.bq \(\chi_{798}(25, \cdot)\) n/a 480 6
798.4.bt \(\chi_{798}(5, \cdot)\) n/a 960 6
798.4.bu \(\chi_{798}(53, \cdot)\) n/a 960 6
798.4.bx \(\chi_{798}(13, \cdot)\) n/a 480 6
798.4.ca \(\chi_{798}(325, \cdot)\) n/a 480 6
798.4.cb \(\chi_{798}(17, \cdot)\) n/a 960 6
798.4.cc \(\chi_{798}(317, \cdot)\) n/a 960 6
798.4.cf \(\chi_{798}(29, \cdot)\) n/a 720 6
798.4.cg \(\chi_{798}(251, \cdot)\) n/a 960 6
798.4.cj \(\chi_{798}(241, \cdot)\) n/a 480 6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(798))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(798)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 2}\)