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Properties

Label 2366.4
Level 2366
Weight 4
Dimension 161328
Nonzero newspaces 30
Sturm bound 1362816
Trace bound 7

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Defining parameters

Level: \( N \) = \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(1362816\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2366))\).

Total New Old
Modular forms 513792 161328 352464
Cusp forms 508320 161328 346992
Eisenstein series 5472 0 5472

Trace form

\( 161328 q + 12 q^{3} - 24 q^{5} - 36 q^{6} + 96 q^{7} + 96 q^{8} + 42 q^{9} + O(q^{10}) \) \( 161328 q + 12 q^{3} - 24 q^{5} - 36 q^{6} + 96 q^{7} + 96 q^{8} + 42 q^{9} - 324 q^{10} - 438 q^{11} - 144 q^{12} - 576 q^{13} - 108 q^{14} - 588 q^{15} + 798 q^{17} + 912 q^{18} + 2676 q^{19} + 408 q^{20} + 168 q^{21} - 216 q^{22} - 1206 q^{23} - 48 q^{24} - 1290 q^{25} - 2736 q^{27} + 696 q^{28} + 4788 q^{29} + 3432 q^{30} + 2466 q^{31} + 1254 q^{33} - 2136 q^{34} - 1980 q^{35} - 3240 q^{36} - 2706 q^{37} - 5364 q^{38} - 2808 q^{39} + 144 q^{40} - 6228 q^{41} - 1548 q^{42} - 1188 q^{43} - 600 q^{44} + 342 q^{45} + 1560 q^{46} + 3390 q^{47} - 96 q^{48} + 3582 q^{49} + 10800 q^{50} + 18894 q^{51} + 1704 q^{52} + 5478 q^{53} + 6480 q^{54} + 1332 q^{55} + 240 q^{56} - 1944 q^{57} - 2880 q^{58} - 4920 q^{59} - 4728 q^{60} - 1812 q^{61} - 8232 q^{62} - 1488 q^{63} - 384 q^{64} + 330 q^{65} - 12288 q^{66} - 7002 q^{67} - 1224 q^{68} - 16836 q^{69} - 3204 q^{70} - 9624 q^{71} - 1440 q^{72} - 17298 q^{73} - 13152 q^{74} - 39366 q^{75} - 10632 q^{76} - 31662 q^{77} + 2160 q^{78} - 8262 q^{79} + 1728 q^{80} + 7572 q^{81} + 8832 q^{82} - 1494 q^{83} + 12528 q^{84} + 33636 q^{85} + 14280 q^{86} + 49728 q^{87} + 1344 q^{88} + 49158 q^{89} + 45588 q^{90} + 25920 q^{91} + 16464 q^{92} + 59382 q^{93} + 36624 q^{94} + 46806 q^{95} - 192 q^{96} + 37392 q^{97} + 16368 q^{98} + 33996 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2366))\)

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
2366.4.a \(\chi_{2366}(1, \cdot)\) 2366.4.a.a 1 1
2366.4.a.b 1
2366.4.a.c 1
2366.4.a.d 1
2366.4.a.e 1
2366.4.a.f 1
2366.4.a.g 1
2366.4.a.h 1
2366.4.a.i 2
2366.4.a.j 2
2366.4.a.k 2
2366.4.a.l 2
2366.4.a.m 3
2366.4.a.n 3
2366.4.a.o 3
2366.4.a.p 3
2366.4.a.q 4
2366.4.a.r 4
2366.4.a.s 5
2366.4.a.t 5
2366.4.a.u 6
2366.4.a.v 6
2366.4.a.w 6
2366.4.a.x 6
2366.4.a.y 7
2366.4.a.z 7
2366.4.a.ba 8
2366.4.a.bb 8
2366.4.a.bc 12
2366.4.a.bd 12
2366.4.a.be 12
2366.4.a.bf 12
2366.4.a.bg 12
2366.4.a.bh 12
2366.4.a.bi 15
2366.4.a.bj 15
2366.4.a.bk 15
2366.4.a.bl 15
2366.4.d \(\chi_{2366}(337, \cdot)\) n/a 232 1
2366.4.e \(\chi_{2366}(529, \cdot)\) n/a 616 2
2366.4.f \(\chi_{2366}(1353, \cdot)\) n/a 620 2
2366.4.g \(\chi_{2366}(1205, \cdot)\) n/a 460 2
2366.4.h \(\chi_{2366}(191, \cdot)\) n/a 616 2
2366.4.i \(\chi_{2366}(2127, \cdot)\) n/a 616 2
2366.4.m \(\chi_{2366}(1037, \cdot)\) n/a 464 2
2366.4.n \(\chi_{2366}(1689, \cdot)\) n/a 616 2
2366.4.o \(\chi_{2366}(23, \cdot)\) n/a 616 2
2366.4.v \(\chi_{2366}(361, \cdot)\) n/a 616 2
2366.4.w \(\chi_{2366}(19, \cdot)\) n/a 1232 4
2366.4.ba \(\chi_{2366}(587, \cdot)\) n/a 1232 4
2366.4.bb \(\chi_{2366}(437, \cdot)\) n/a 1232 4
2366.4.bc \(\chi_{2366}(89, \cdot)\) n/a 1232 4
2366.4.be \(\chi_{2366}(183, \cdot)\) n/a 3288 12
2366.4.bf \(\chi_{2366}(155, \cdot)\) n/a 3264 12
2366.4.bi \(\chi_{2366}(9, \cdot)\) n/a 8736 24
2366.4.bj \(\chi_{2366}(29, \cdot)\) n/a 6576 24
2366.4.bk \(\chi_{2366}(53, \cdot)\) n/a 8736 24
2366.4.bl \(\chi_{2366}(107, \cdot)\) n/a 8736 24
2366.4.bn \(\chi_{2366}(83, \cdot)\) n/a 8736 24
2366.4.bo \(\chi_{2366}(121, \cdot)\) n/a 8736 24
2366.4.bv \(\chi_{2366}(95, \cdot)\) n/a 8736 24
2366.4.bw \(\chi_{2366}(25, \cdot)\) n/a 8736 24
2366.4.bx \(\chi_{2366}(43, \cdot)\) n/a 6528 24
2366.4.cb \(\chi_{2366}(45, \cdot)\) n/a 17472 48
2366.4.cc \(\chi_{2366}(5, \cdot)\) n/a 17472 48
2366.4.cd \(\chi_{2366}(41, \cdot)\) n/a 17472 48
2366.4.ch \(\chi_{2366}(33, \cdot)\) n/a 17472 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2366))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2366)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 2}\)