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Properties

Label 1862.4
Level 1862
Weight 4
Dimension 101001
Nonzero newspaces 32
Sturm bound 846720
Trace bound 12

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Defining parameters

Level: \( N \) = \( 1862 = 2 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(846720\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1862))\).

Total New Old
Modular forms 319680 101001 218679
Cusp forms 315360 101001 214359
Eisenstein series 4320 0 4320

Trace form

\( 101001 q + 48 q^{3} - 96 q^{5} - 144 q^{6} - 96 q^{7} + 168 q^{9} + O(q^{10}) \) \( 101001 q + 48 q^{3} - 96 q^{5} - 144 q^{6} - 96 q^{7} + 168 q^{9} + 144 q^{10} + 168 q^{11} + 336 q^{12} + 552 q^{13} + 264 q^{14} - 264 q^{15} - 888 q^{17} - 1158 q^{18} - 876 q^{19} - 768 q^{20} - 144 q^{21} - 1026 q^{22} - 1140 q^{23} - 192 q^{24} + 1704 q^{25} + 2076 q^{26} + 4257 q^{27} + 240 q^{28} + 2934 q^{29} + 672 q^{30} + 930 q^{31} - 3198 q^{33} - 1632 q^{34} - 840 q^{35} - 672 q^{36} - 9906 q^{37} - 2388 q^{38} - 11130 q^{39} - 1440 q^{40} - 4962 q^{41} + 1656 q^{42} + 1464 q^{43} + 3924 q^{44} + 19938 q^{45} + 11856 q^{46} + 10446 q^{47} + 1104 q^{48} + 15948 q^{49} + 6816 q^{50} + 17613 q^{51} + 2040 q^{52} + 6744 q^{53} + 1260 q^{54} + 3960 q^{55} - 576 q^{56} - 6432 q^{57} - 11016 q^{58} - 15972 q^{59} - 10656 q^{60} - 19590 q^{61} - 12180 q^{62} - 18240 q^{63} + 1536 q^{64} - 5994 q^{65} + 912 q^{66} - 6072 q^{67} - 1716 q^{68} + 72 q^{69} - 1512 q^{70} + 4158 q^{71} - 1032 q^{72} - 2943 q^{73} + 6048 q^{74} - 2214 q^{75} + 2928 q^{76} + 4452 q^{77} + 11016 q^{78} + 6810 q^{79} - 1536 q^{80} - 23943 q^{81} - 1704 q^{82} - 17298 q^{83} - 1824 q^{84} - 9240 q^{85} + 2568 q^{86} + 1428 q^{87} + 5376 q^{88} + 11910 q^{89} + 2892 q^{90} + 11052 q^{91} - 4896 q^{92} + 28122 q^{93} - 10032 q^{94} + 14340 q^{95} - 768 q^{96} + 372 q^{97} - 5280 q^{98} + 12447 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1862))\)

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
1862.4.a \(\chi_{1862}(1, \cdot)\) 1862.4.a.a 1 1
1862.4.a.b 2
1862.4.a.c 2
1862.4.a.d 2
1862.4.a.e 2
1862.4.a.f 2
1862.4.a.g 2
1862.4.a.h 4
1862.4.a.i 4
1862.4.a.j 5
1862.4.a.k 5
1862.4.a.l 6
1862.4.a.m 6
1862.4.a.n 7
1862.4.a.o 7
1862.4.a.p 7
1862.4.a.q 7
1862.4.a.r 8
1862.4.a.s 8
1862.4.a.t 10
1862.4.a.u 10
1862.4.a.v 11
1862.4.a.w 11
1862.4.a.x 14
1862.4.a.y 14
1862.4.a.z 14
1862.4.a.ba 14
1862.4.d \(\chi_{1862}(1861, \cdot)\) n/a 200 1
1862.4.e \(\chi_{1862}(1255, \cdot)\) n/a 360 2
1862.4.f \(\chi_{1862}(197, \cdot)\) n/a 410 2
1862.4.g \(\chi_{1862}(1341, \cdot)\) n/a 400 2
1862.4.h \(\chi_{1862}(961, \cdot)\) n/a 400 2
1862.4.k \(\chi_{1862}(411, \cdot)\) n/a 400 2
1862.4.l \(\chi_{1862}(227, \cdot)\) n/a 400 2
1862.4.m \(\chi_{1862}(293, \cdot)\) n/a 400 2
1862.4.t \(\chi_{1862}(31, \cdot)\) n/a 400 2
1862.4.u \(\chi_{1862}(267, \cdot)\) n/a 1512 6
1862.4.v \(\chi_{1862}(99, \cdot)\) n/a 1230 6
1862.4.w \(\chi_{1862}(177, \cdot)\) n/a 1200 6
1862.4.x \(\chi_{1862}(557, \cdot)\) n/a 1200 6
1862.4.y \(\chi_{1862}(265, \cdot)\) n/a 1680 6
1862.4.bb \(\chi_{1862}(97, \cdot)\) n/a 1200 6
1862.4.bc \(\chi_{1862}(325, \cdot)\) n/a 1200 6
1862.4.bh \(\chi_{1862}(117, \cdot)\) n/a 1200 6
1862.4.bk \(\chi_{1862}(163, \cdot)\) n/a 3360 12
1862.4.bl \(\chi_{1862}(11, \cdot)\) n/a 3360 12
1862.4.bm \(\chi_{1862}(239, \cdot)\) n/a 3360 12
1862.4.bn \(\chi_{1862}(39, \cdot)\) n/a 3024 12
1862.4.bo \(\chi_{1862}(103, \cdot)\) n/a 3360 12
1862.4.bv \(\chi_{1862}(27, \cdot)\) n/a 3360 12
1862.4.bw \(\chi_{1862}(75, \cdot)\) n/a 3360 12
1862.4.bx \(\chi_{1862}(145, \cdot)\) n/a 3360 12
1862.4.ca \(\chi_{1862}(25, \cdot)\) n/a 10080 36
1862.4.cb \(\chi_{1862}(43, \cdot)\) n/a 10080 36
1862.4.cc \(\chi_{1862}(9, \cdot)\) n/a 10080 36
1862.4.cf \(\chi_{1862}(33, \cdot)\) n/a 10080 36
1862.4.ck \(\chi_{1862}(13, \cdot)\) n/a 10080 36
1862.4.cl \(\chi_{1862}(3, \cdot)\) n/a 10080 36

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1862))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1862)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(931))\)\(^{\oplus 2}\)