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Properties

Label 1183.4
Level 1183
Weight 4
Dimension 160305
Nonzero newspaces 30
Sturm bound 454272
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(454272\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1183))\).

Total New Old
Modular forms 171720 162349 9371
Cusp forms 168984 160305 8679
Eisenstein series 2736 2044 692

Trace form

\( 160305 q - 267 q^{2} - 273 q^{3} - 267 q^{4} - 255 q^{5} - 234 q^{6} - 381 q^{7} - 981 q^{8} - 309 q^{9} + O(q^{10}) \) \( 160305 q - 267 q^{2} - 273 q^{3} - 267 q^{4} - 255 q^{5} - 234 q^{6} - 381 q^{7} - 981 q^{8} - 309 q^{9} + 66 q^{10} - 27 q^{11} + 714 q^{12} - 369 q^{14} - 306 q^{15} - 207 q^{16} - 945 q^{17} - 3597 q^{18} - 2199 q^{19} - 2496 q^{20} - 561 q^{21} + 888 q^{22} + 855 q^{23} + 4098 q^{24} + 1419 q^{25} + 1212 q^{26} + 2838 q^{27} - 249 q^{28} - 2370 q^{29} - 2634 q^{30} - 1647 q^{31} - 3201 q^{32} - 2613 q^{33} - 3186 q^{34} - 393 q^{35} - 1299 q^{36} + 3 q^{37} + 5196 q^{38} - 144 q^{39} - 960 q^{40} - 1266 q^{41} - 1212 q^{42} - 2460 q^{43} + 708 q^{44} + 354 q^{45} + 3318 q^{46} + 63 q^{47} - 2106 q^{48} + 1761 q^{49} - 1479 q^{50} - 1785 q^{51} - 948 q^{52} + 2823 q^{53} + 2610 q^{54} + 5154 q^{55} + 897 q^{56} + 4902 q^{57} + 3834 q^{58} + 2619 q^{59} + 4788 q^{60} - 4863 q^{61} - 10152 q^{62} - 6375 q^{63} - 18675 q^{64} - 8406 q^{65} - 17010 q^{66} - 4083 q^{67} + 4578 q^{68} + 5526 q^{69} + 3264 q^{70} + 5484 q^{71} + 27255 q^{72} + 13971 q^{73} + 36048 q^{74} + 27678 q^{75} + 38850 q^{76} + 20529 q^{77} + 14676 q^{78} + 8295 q^{79} + 25584 q^{80} + 2844 q^{81} + 2718 q^{82} + 7002 q^{83} - 28332 q^{84} - 21942 q^{85} - 31512 q^{86} - 49746 q^{87} - 74832 q^{88} - 39429 q^{89} - 91728 q^{90} - 17124 q^{91} - 70212 q^{92} - 44277 q^{93} - 64662 q^{94} - 30351 q^{95} - 46686 q^{96} - 15222 q^{97} - 10425 q^{98} + 12312 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1183))\)

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
1183.4.a \(\chi_{1183}(1, \cdot)\) 1183.4.a.a 1 1
1183.4.a.b 1
1183.4.a.c 1
1183.4.a.d 3
1183.4.a.e 4
1183.4.a.f 5
1183.4.a.g 6
1183.4.a.h 9
1183.4.a.i 9
1183.4.a.j 10
1183.4.a.k 10
1183.4.a.l 11
1183.4.a.m 11
1183.4.a.n 22
1183.4.a.o 22
1183.4.a.p 24
1183.4.a.q 24
1183.4.a.r 30
1183.4.a.s 30
1183.4.c \(\chi_{1183}(337, \cdot)\) n/a 230 1
1183.4.e \(\chi_{1183}(170, \cdot)\) n/a 598 2
1183.4.f \(\chi_{1183}(22, \cdot)\) n/a 464 2
1183.4.g \(\chi_{1183}(191, \cdot)\) n/a 596 2
1183.4.h \(\chi_{1183}(529, \cdot)\) n/a 596 2
1183.4.i \(\chi_{1183}(944, \cdot)\) n/a 596 2
1183.4.k \(\chi_{1183}(23, \cdot)\) n/a 596 2
1183.4.q \(\chi_{1183}(316, \cdot)\) n/a 460 2
1183.4.r \(\chi_{1183}(506, \cdot)\) n/a 596 2
1183.4.u \(\chi_{1183}(361, \cdot)\) n/a 596 2
1183.4.w \(\chi_{1183}(19, \cdot)\) n/a 1192 4
1183.4.ba \(\chi_{1183}(89, \cdot)\) n/a 1192 4
1183.4.bb \(\chi_{1183}(437, \cdot)\) n/a 1192 4
1183.4.bc \(\chi_{1183}(188, \cdot)\) n/a 1192 4
1183.4.be \(\chi_{1183}(92, \cdot)\) n/a 3264 12
1183.4.bg \(\chi_{1183}(64, \cdot)\) n/a 3288 12
1183.4.bi \(\chi_{1183}(16, \cdot)\) n/a 8688 24
1183.4.bj \(\chi_{1183}(9, \cdot)\) n/a 8688 24
1183.4.bk \(\chi_{1183}(29, \cdot)\) n/a 6528 24
1183.4.bl \(\chi_{1183}(53, \cdot)\) n/a 8688 24
1183.4.bn \(\chi_{1183}(34, \cdot)\) n/a 8688 24
1183.4.bp \(\chi_{1183}(30, \cdot)\) n/a 8688 24
1183.4.bs \(\chi_{1183}(25, \cdot)\) n/a 8688 24
1183.4.bt \(\chi_{1183}(36, \cdot)\) n/a 6576 24
1183.4.bz \(\chi_{1183}(4, \cdot)\) n/a 8688 24
1183.4.cb \(\chi_{1183}(6, \cdot)\) n/a 17376 48
1183.4.cc \(\chi_{1183}(5, \cdot)\) n/a 17376 48
1183.4.cd \(\chi_{1183}(45, \cdot)\) n/a 17376 48
1183.4.ch \(\chi_{1183}(24, \cdot)\) n/a 17376 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1183))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1183)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)