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Properties

Label 1863.2
Level 1863
Weight 2
Dimension 99816
Nonzero newspaces 16
Sturm bound 513216
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1863 = 3^{4} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(513216\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1863))\).

Total New Old
Modular forms 130680 102168 28512
Cusp forms 125929 99816 26113
Eisenstein series 4751 2352 2399

Trace form

\( 99816 q - 240 q^{2} - 360 q^{3} - 396 q^{4} - 234 q^{5} - 360 q^{6} - 394 q^{7} - 216 q^{8} - 360 q^{9} + O(q^{10}) \) \( 99816 q - 240 q^{2} - 360 q^{3} - 396 q^{4} - 234 q^{5} - 360 q^{6} - 394 q^{7} - 216 q^{8} - 360 q^{9} - 560 q^{10} - 222 q^{11} - 360 q^{12} - 382 q^{13} - 198 q^{14} - 360 q^{15} - 396 q^{16} - 210 q^{17} - 378 q^{18} - 592 q^{19} - 306 q^{20} - 414 q^{21} - 410 q^{22} - 285 q^{23} - 864 q^{24} - 420 q^{25} - 414 q^{26} - 414 q^{27} - 628 q^{28} - 294 q^{29} - 468 q^{30} - 418 q^{31} - 336 q^{32} - 414 q^{33} - 422 q^{34} - 258 q^{35} - 432 q^{36} - 556 q^{37} - 162 q^{38} - 360 q^{39} - 446 q^{40} - 234 q^{41} - 450 q^{42} - 394 q^{43} - 366 q^{44} - 468 q^{45} - 653 q^{46} - 630 q^{47} - 558 q^{48} - 440 q^{49} - 528 q^{50} - 486 q^{51} - 478 q^{52} - 390 q^{53} - 612 q^{54} - 668 q^{55} - 582 q^{56} - 468 q^{57} - 446 q^{58} - 378 q^{59} - 594 q^{60} - 430 q^{61} - 450 q^{62} - 468 q^{63} - 606 q^{64} - 258 q^{65} - 360 q^{66} - 418 q^{67} - 48 q^{68} - 324 q^{69} - 922 q^{70} - 30 q^{71} + 72 q^{72} - 502 q^{73} + 126 q^{74} - 180 q^{75} - 442 q^{76} + 90 q^{77} - 126 q^{78} - 394 q^{79} + 396 q^{80} - 216 q^{81} - 992 q^{82} - 6 q^{83} + 90 q^{84} - 458 q^{85} + 162 q^{86} - 72 q^{87} - 506 q^{88} - 84 q^{89} - 198 q^{90} - 570 q^{91} - 159 q^{92} - 792 q^{93} - 482 q^{94} - 366 q^{95} - 342 q^{96} - 502 q^{97} - 516 q^{98} - 504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1863))\)

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
1863.2.a \(\chi_{1863}(1, \cdot)\) 1863.2.a.a 6 1
1863.2.a.b 6
1863.2.a.c 6
1863.2.a.d 6
1863.2.a.e 8
1863.2.a.f 8
1863.2.a.g 10
1863.2.a.h 10
1863.2.a.i 14
1863.2.a.j 14
1863.2.c \(\chi_{1863}(1862, \cdot)\) 1863.2.c.a 12 1
1863.2.c.b 32
1863.2.c.c 48
1863.2.e \(\chi_{1863}(622, \cdot)\) n/a 176 2
1863.2.g \(\chi_{1863}(620, \cdot)\) n/a 188 2
1863.2.i \(\chi_{1863}(208, \cdot)\) n/a 396 6
1863.2.j \(\chi_{1863}(82, \cdot)\) n/a 920 10
1863.2.m \(\chi_{1863}(206, \cdot)\) n/a 420 6
1863.2.o \(\chi_{1863}(80, \cdot)\) n/a 920 10
1863.2.q \(\chi_{1863}(70, \cdot)\) n/a 3564 18
1863.2.r \(\chi_{1863}(55, \cdot)\) n/a 1880 20
1863.2.u \(\chi_{1863}(68, \cdot)\) n/a 3852 18
1863.2.w \(\chi_{1863}(53, \cdot)\) n/a 1880 20
1863.2.y \(\chi_{1863}(64, \cdot)\) n/a 4200 60
1863.2.z \(\chi_{1863}(17, \cdot)\) n/a 4200 60
1863.2.bc \(\chi_{1863}(4, \cdot)\) n/a 38520 180
1863.2.bd \(\chi_{1863}(5, \cdot)\) n/a 38520 180

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1863))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1863)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(621))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1863))\)\(^{\oplus 1}\)