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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

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

Display 100 coefficients 10 coefficients

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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(1183)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 1}\)