Properties

Label 1183.2
Level 1183
Weight 2
Dimension 52755
Nonzero newspaces 30
Sturm bound 227136
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(227136\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1183))\).

Total New Old
Modular forms 58152 54799 3353
Cusp forms 55417 52755 2662
Eisenstein series 2735 2044 691

Trace form

\( 52755q - 261q^{2} - 260q^{3} - 257q^{4} - 258q^{5} - 252q^{6} - 333q^{7} - 681q^{8} - 283q^{9} + O(q^{10}) \) \( 52755q - 261q^{2} - 260q^{3} - 257q^{4} - 258q^{5} - 252q^{6} - 333q^{7} - 681q^{8} - 283q^{9} - 306q^{10} - 276q^{11} - 340q^{12} - 312q^{13} - 651q^{14} - 684q^{15} - 313q^{16} - 282q^{17} - 357q^{18} - 324q^{19} - 354q^{20} - 378q^{21} - 744q^{22} - 288q^{23} - 444q^{24} - 317q^{25} - 348q^{26} - 608q^{27} - 423q^{28} - 738q^{29} - 480q^{30} - 336q^{31} - 465q^{32} - 384q^{33} - 402q^{34} - 408q^{35} - 905q^{36} - 294q^{37} - 372q^{38} - 352q^{39} - 702q^{40} - 402q^{41} - 498q^{42} - 800q^{43} - 492q^{44} - 486q^{45} - 528q^{46} - 384q^{47} - 572q^{48} - 445q^{49} - 939q^{50} - 504q^{51} - 454q^{52} - 642q^{53} - 552q^{54} - 456q^{55} - 543q^{56} - 876q^{57} - 474q^{58} - 372q^{59} - 744q^{60} - 430q^{61} - 504q^{62} - 513q^{63} - 1025q^{64} - 450q^{65} - 888q^{66} - 420q^{67} - 630q^{68} - 480q^{69} - 588q^{70} - 828q^{71} - 381q^{72} - 438q^{73} - 498q^{74} - 460q^{75} - 300q^{76} - 282q^{77} - 924q^{78} - 376q^{79} - 282q^{80} - 247q^{81} - 6q^{82} - 276q^{83} - 66q^{84} - 492q^{85} - 348q^{86} - 192q^{87} + 84q^{88} - 270q^{89} - 126q^{90} - 302q^{91} - 1092q^{92} - 360q^{93} + 24q^{94} - 288q^{95} - 132q^{96} - 54q^{97} - 243q^{98} - 672q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1183.2.a \(\chi_{1183}(1, \cdot)\) 1183.2.a.a 1 1
1183.2.a.b 1
1183.2.a.c 2
1183.2.a.d 2
1183.2.a.e 2
1183.2.a.f 2
1183.2.a.g 2
1183.2.a.h 3
1183.2.a.i 3
1183.2.a.j 3
1183.2.a.k 4
1183.2.a.l 4
1183.2.a.m 6
1183.2.a.n 6
1183.2.a.o 6
1183.2.a.p 6
1183.2.a.q 12
1183.2.a.r 12
1183.2.c \(\chi_{1183}(337, \cdot)\) 1183.2.c.a 2 1
1183.2.c.b 2
1183.2.c.c 4
1183.2.c.d 4
1183.2.c.e 4
1183.2.c.f 6
1183.2.c.g 8
1183.2.c.h 12
1183.2.c.i 12
1183.2.c.j 24
1183.2.e \(\chi_{1183}(170, \cdot)\) 1183.2.e.a 2 2
1183.2.e.b 2
1183.2.e.c 2
1183.2.e.d 4
1183.2.e.e 4
1183.2.e.f 10
1183.2.e.g 12
1183.2.e.h 12
1183.2.e.i 16
1183.2.e.j 24
1183.2.e.k 48
1183.2.e.l 48
1183.2.f \(\chi_{1183}(22, \cdot)\) n/a 152 2
1183.2.g \(\chi_{1183}(191, \cdot)\) n/a 186 2
1183.2.h \(\chi_{1183}(529, \cdot)\) n/a 186 2
1183.2.i \(\chi_{1183}(944, \cdot)\) n/a 188 2
1183.2.k \(\chi_{1183}(23, \cdot)\) n/a 186 2
1183.2.q \(\chi_{1183}(316, \cdot)\) n/a 156 2
1183.2.r \(\chi_{1183}(506, \cdot)\) n/a 184 2
1183.2.u \(\chi_{1183}(361, \cdot)\) n/a 186 2
1183.2.w \(\chi_{1183}(19, \cdot)\) n/a 372 4
1183.2.ba \(\chi_{1183}(89, \cdot)\) n/a 372 4
1183.2.bb \(\chi_{1183}(437, \cdot)\) n/a 368 4
1183.2.bc \(\chi_{1183}(188, \cdot)\) n/a 368 4
1183.2.be \(\chi_{1183}(92, \cdot)\) n/a 1104 12
1183.2.bg \(\chi_{1183}(64, \cdot)\) n/a 1080 12
1183.2.bi \(\chi_{1183}(16, \cdot)\) n/a 2856 24
1183.2.bj \(\chi_{1183}(9, \cdot)\) n/a 2856 24
1183.2.bk \(\chi_{1183}(29, \cdot)\) n/a 2208 24
1183.2.bl \(\chi_{1183}(53, \cdot)\) n/a 2880 24
1183.2.bn \(\chi_{1183}(34, \cdot)\) n/a 2832 24
1183.2.bp \(\chi_{1183}(30, \cdot)\) n/a 2856 24
1183.2.bs \(\chi_{1183}(25, \cdot)\) n/a 2880 24
1183.2.bt \(\chi_{1183}(36, \cdot)\) n/a 2160 24
1183.2.bz \(\chi_{1183}(4, \cdot)\) n/a 2856 24
1183.2.cb \(\chi_{1183}(6, \cdot)\) n/a 5760 48
1183.2.cc \(\chi_{1183}(5, \cdot)\) n/a 5760 48
1183.2.cd \(\chi_{1183}(45, \cdot)\) n/a 5712 48
1183.2.ch \(\chi_{1183}(24, \cdot)\) n/a 5712 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1183))\) into lower level spaces

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