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Properties

Label 1134.3
Level 1134
Weight 3
Dimension 17664
Nonzero newspaces 22
Sturm bound 209952
Trace bound 23

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Defining parameters

Level: \( N \) = \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 22 \)
Sturm bound: \(209952\)
Trace bound: \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1134))\).

Total New Old
Modular forms 71280 17664 53616
Cusp forms 68688 17664 51024
Eisenstein series 2592 0 2592

Trace form

\( 17664 q + 36 q^{5} + 6 q^{7} + O(q^{10}) \) \( 17664 q + 36 q^{5} + 6 q^{7} - 24 q^{10} - 36 q^{11} - 12 q^{13} - 36 q^{14} - 144 q^{18} - 360 q^{19} - 360 q^{20} - 270 q^{21} - 168 q^{22} - 684 q^{23} - 180 q^{25} + 108 q^{27} + 48 q^{28} + 612 q^{29} + 432 q^{30} + 468 q^{31} + 756 q^{33} + 456 q^{34} + 972 q^{35} + 360 q^{36} + 672 q^{37} + 576 q^{38} + 48 q^{40} - 612 q^{41} - 468 q^{43} - 864 q^{45} - 48 q^{46} - 1404 q^{47} - 678 q^{49} - 864 q^{50} - 252 q^{51} - 336 q^{52} - 1620 q^{53} - 648 q^{55} - 72 q^{56} + 432 q^{57} - 456 q^{58} + 720 q^{59} + 720 q^{61} + 540 q^{63} + 96 q^{64} + 4248 q^{65} + 2016 q^{66} - 144 q^{67} + 720 q^{68} + 3744 q^{69} + 300 q^{70} + 2592 q^{71} + 1152 q^{72} + 1308 q^{73} + 2016 q^{74} + 1800 q^{75} + 168 q^{76} + 2142 q^{77} + 576 q^{78} + 600 q^{79} - 288 q^{81} + 192 q^{82} + 324 q^{83} - 144 q^{84} + 1440 q^{85} - 648 q^{86} - 4032 q^{87} + 336 q^{88} - 2268 q^{89} - 2880 q^{90} - 330 q^{91} - 936 q^{92} - 4248 q^{93} + 1368 q^{94} - 5112 q^{95} - 576 q^{96} + 996 q^{97} - 648 q^{98} - 3600 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1134))\)

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
1134.3.b \(\chi_{1134}(323, \cdot)\) 1134.3.b.a 8 1
1134.3.b.b 16
1134.3.b.c 24
1134.3.c \(\chi_{1134}(811, \cdot)\) 1134.3.c.a 8 1
1134.3.c.b 8
1134.3.c.c 16
1134.3.c.d 16
1134.3.c.e 16
1134.3.i \(\chi_{1134}(53, \cdot)\) n/a 128 2
1134.3.j \(\chi_{1134}(1027, \cdot)\) n/a 128 2
1134.3.n \(\chi_{1134}(325, \cdot)\) n/a 128 2
1134.3.o \(\chi_{1134}(55, \cdot)\) n/a 128 2
1134.3.p \(\chi_{1134}(271, \cdot)\) n/a 128 2
1134.3.q \(\chi_{1134}(701, \cdot)\) 1134.3.q.a 8 2
1134.3.q.b 8
1134.3.q.c 8
1134.3.q.d 8
1134.3.q.e 16
1134.3.q.f 16
1134.3.q.g 32
1134.3.r \(\chi_{1134}(431, \cdot)\) n/a 128 2
1134.3.s \(\chi_{1134}(485, \cdot)\) n/a 128 2
1134.3.x \(\chi_{1134}(73, \cdot)\) n/a 288 6
1134.3.y \(\chi_{1134}(233, \cdot)\) n/a 288 6
1134.3.bb \(\chi_{1134}(71, \cdot)\) n/a 216 6
1134.3.bc \(\chi_{1134}(179, \cdot)\) n/a 288 6
1134.3.bd \(\chi_{1134}(181, \cdot)\) n/a 288 6
1134.3.be \(\chi_{1134}(19, \cdot)\) n/a 288 6
1134.3.bj \(\chi_{1134}(11, \cdot)\) n/a 2592 18
1134.3.bl \(\chi_{1134}(31, \cdot)\) n/a 2592 18
1134.3.bm \(\chi_{1134}(13, \cdot)\) n/a 2592 18
1134.3.bn \(\chi_{1134}(65, \cdot)\) n/a 2592 18
1134.3.bo \(\chi_{1134}(29, \cdot)\) n/a 1944 18
1134.3.br \(\chi_{1134}(103, \cdot)\) n/a 2592 18

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1134))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1134)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(567))\)\(^{\oplus 2}\)