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Properties

Label 2178.3
Level 2178
Weight 3
Dimension 67836
Nonzero newspaces 16
Sturm bound 784080
Trace bound 5

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Defining parameters

Level: \( N \) = \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(784080\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2178))\).

Total New Old
Modular forms 263920 67836 196084
Cusp forms 258800 67836 190964
Eisenstein series 5120 0 5120

Trace form

\( 67836 q - 18 q^{5} - 12 q^{6} + 54 q^{7} + 12 q^{9} + O(q^{10}) \) \( 67836 q - 18 q^{5} - 12 q^{6} + 54 q^{7} + 12 q^{9} + 12 q^{10} - 10 q^{11} + 12 q^{12} - 54 q^{13} - 44 q^{14} + 18 q^{15} - 60 q^{17} - 24 q^{18} - 12 q^{19} - 36 q^{20} - 42 q^{21} - 562 q^{23} - 160 q^{24} - 982 q^{25} - 720 q^{26} - 600 q^{27} - 216 q^{28} - 682 q^{29} - 168 q^{30} - 194 q^{31} + 100 q^{33} + 300 q^{34} + 1060 q^{35} + 92 q^{36} + 660 q^{37} + 1008 q^{38} + 738 q^{39} + 456 q^{40} + 1534 q^{41} + 752 q^{42} + 1634 q^{43} + 280 q^{44} + 466 q^{45} + 344 q^{46} + 394 q^{47} + 24 q^{48} + 302 q^{49} + 160 q^{50} - 352 q^{51} + 68 q^{52} - 1380 q^{53} + 36 q^{54} - 760 q^{55} + 72 q^{56} - 1136 q^{57} - 308 q^{58} - 1434 q^{59} - 36 q^{60} - 578 q^{61} - 40 q^{62} - 98 q^{63} - 48 q^{64} + 90 q^{65} - 30 q^{67} - 48 q^{68} + 658 q^{69} - 116 q^{70} + 1840 q^{71} - 96 q^{72} + 1180 q^{73} + 152 q^{74} + 1388 q^{75} + 24 q^{76} + 1510 q^{77} + 144 q^{78} + 1362 q^{79} - 80 q^{80} + 3748 q^{81} - 1668 q^{82} + 2442 q^{83} + 2096 q^{84} - 1420 q^{85} + 1812 q^{86} + 4346 q^{87} - 120 q^{88} + 2140 q^{89} + 3200 q^{90} - 2712 q^{91} + 1116 q^{92} + 2222 q^{93} - 276 q^{94} + 1800 q^{95} + 48 q^{96} + 726 q^{97} - 320 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2178))\)

We only show spaces with odd 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
2178.3.c \(\chi_{2178}(485, \cdot)\) 2178.3.c.a 2 1
2178.3.c.b 2
2178.3.c.c 2
2178.3.c.d 2
2178.3.c.e 2
2178.3.c.f 4
2178.3.c.g 4
2178.3.c.h 4
2178.3.c.i 4
2178.3.c.j 4
2178.3.c.k 6
2178.3.c.l 6
2178.3.c.m 8
2178.3.c.n 8
2178.3.c.o 8
2178.3.c.p 8
2178.3.d \(\chi_{2178}(1693, \cdot)\) 2178.3.d.a 2 1
2178.3.d.b 2
2178.3.d.c 2
2178.3.d.d 4
2178.3.d.e 4
2178.3.d.f 4
2178.3.d.g 4
2178.3.d.h 4
2178.3.d.i 8
2178.3.d.j 8
2178.3.d.k 8
2178.3.d.l 8
2178.3.d.m 16
2178.3.d.n 16
2178.3.g \(\chi_{2178}(241, \cdot)\) n/a 432 2
2178.3.h \(\chi_{2178}(1211, \cdot)\) n/a 436 2
2178.3.j \(\chi_{2178}(1207, \cdot)\) n/a 360 4
2178.3.k \(\chi_{2178}(251, \cdot)\) n/a 288 4
2178.3.o \(\chi_{2178}(109, \cdot)\) n/a 1100 10
2178.3.p \(\chi_{2178}(89, \cdot)\) n/a 880 10
2178.3.s \(\chi_{2178}(245, \cdot)\) n/a 1728 8
2178.3.t \(\chi_{2178}(403, \cdot)\) n/a 1728 8
2178.3.x \(\chi_{2178}(23, \cdot)\) n/a 5280 20
2178.3.y \(\chi_{2178}(43, \cdot)\) n/a 5280 20
2178.3.ba \(\chi_{2178}(53, \cdot)\) n/a 3520 40
2178.3.bb \(\chi_{2178}(19, \cdot)\) n/a 4400 40
2178.3.bd \(\chi_{2178}(7, \cdot)\) n/a 21120 80
2178.3.be \(\chi_{2178}(5, \cdot)\) n/a 21120 80

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2178))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2178)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 2}\)