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Properties

Label 2106.2
Level 2106
Weight 2
Dimension 31872
Nonzero newspaces 33
Sturm bound 489888
Trace bound 45

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Defining parameters

Level: \( N \) = \( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 33 \)
Sturm bound: \(489888\)
Trace bound: \(45\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2106))\).

Total New Old
Modular forms 125064 31872 93192
Cusp forms 119881 31872 88009
Eisenstein series 5183 0 5183

Trace form

\( 31872 q - 12 q^{5} - 12 q^{7} - 6 q^{8} + O(q^{10}) \) \( 31872 q - 12 q^{5} - 12 q^{7} - 6 q^{8} - 12 q^{10} - 30 q^{11} - 12 q^{13} - 12 q^{14} - 24 q^{17} + 18 q^{18} + 36 q^{19} + 60 q^{20} + 108 q^{21} + 42 q^{22} + 156 q^{23} + 72 q^{25} + 90 q^{26} + 108 q^{27} + 48 q^{28} + 168 q^{29} + 108 q^{30} + 72 q^{31} + 108 q^{33} + 30 q^{34} + 120 q^{35} + 36 q^{36} + 12 q^{37} - 6 q^{38} - 12 q^{40} + 6 q^{41} - 18 q^{43} - 12 q^{44} + 108 q^{45} - 24 q^{46} + 108 q^{47} + 24 q^{49} - 72 q^{50} + 126 q^{51} - 12 q^{52} + 60 q^{53} + 72 q^{55} - 12 q^{56} + 108 q^{57} - 48 q^{58} + 138 q^{59} + 36 q^{61} - 48 q^{62} + 108 q^{63} - 6 q^{64} - 12 q^{65} - 144 q^{66} + 90 q^{67} - 60 q^{68} - 252 q^{69} + 48 q^{70} - 240 q^{71} - 144 q^{72} - 84 q^{73} - 228 q^{74} - 360 q^{75} + 30 q^{76} - 492 q^{77} - 144 q^{78} + 120 q^{79} - 48 q^{80} - 288 q^{81} - 12 q^{82} - 288 q^{83} - 72 q^{84} + 72 q^{85} - 234 q^{86} - 576 q^{87} + 42 q^{88} - 348 q^{89} - 288 q^{90} - 30 q^{91} - 132 q^{92} - 252 q^{93} + 36 q^{94} - 168 q^{95} - 36 q^{96} + 102 q^{97} - 30 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2106))\)

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
2106.2.a \(\chi_{2106}(1, \cdot)\) 2106.2.a.a 1 1
2106.2.a.b 1
2106.2.a.c 1
2106.2.a.d 1
2106.2.a.e 1
2106.2.a.f 1
2106.2.a.g 2
2106.2.a.h 2
2106.2.a.i 2
2106.2.a.j 2
2106.2.a.k 2
2106.2.a.l 2
2106.2.a.m 2
2106.2.a.n 2
2106.2.a.o 2
2106.2.a.p 2
2106.2.a.q 3
2106.2.a.r 3
2106.2.a.s 4
2106.2.a.t 4
2106.2.a.u 4
2106.2.a.v 4
2106.2.b \(\chi_{2106}(649, \cdot)\) 2106.2.b.a 6 1
2106.2.b.b 6
2106.2.b.c 14
2106.2.b.d 14
2106.2.b.e 16
2106.2.e \(\chi_{2106}(703, \cdot)\) 2106.2.e.a 2 2
2106.2.e.b 2
2106.2.e.c 2
2106.2.e.d 2
2106.2.e.e 2
2106.2.e.f 2
2106.2.e.g 2
2106.2.e.h 2
2106.2.e.i 2
2106.2.e.j 2
2106.2.e.k 2
2106.2.e.l 2
2106.2.e.m 2
2106.2.e.n 2
2106.2.e.o 2
2106.2.e.p 2
2106.2.e.q 2
2106.2.e.r 2
2106.2.e.s 2
2106.2.e.t 2
2106.2.e.u 2
2106.2.e.v 2
2106.2.e.w 2
2106.2.e.x 2
2106.2.e.y 2
2106.2.e.z 2
2106.2.e.ba 2
2106.2.e.bb 2
2106.2.e.bc 4
2106.2.e.bd 4
2106.2.e.be 4
2106.2.e.bf 4
2106.2.e.bg 4
2106.2.e.bh 4
2106.2.e.bi 8
2106.2.e.bj 8
2106.2.f \(\chi_{2106}(55, \cdot)\) n/a 112 2
2106.2.g \(\chi_{2106}(217, \cdot)\) n/a 112 2
2106.2.h \(\chi_{2106}(1459, \cdot)\) n/a 112 2
2106.2.j \(\chi_{2106}(161, \cdot)\) n/a 112 2
2106.2.l \(\chi_{2106}(1135, \cdot)\) n/a 112 2
2106.2.p \(\chi_{2106}(595, \cdot)\) n/a 112 2
2106.2.s \(\chi_{2106}(433, \cdot)\) n/a 112 2
2106.2.t \(\chi_{2106}(1351, \cdot)\) n/a 112 2
2106.2.w \(\chi_{2106}(235, \cdot)\) n/a 216 6
2106.2.x \(\chi_{2106}(451, \cdot)\) n/a 252 6
2106.2.y \(\chi_{2106}(289, \cdot)\) n/a 252 6
2106.2.ba \(\chi_{2106}(323, \cdot)\) n/a 224 4
2106.2.bb \(\chi_{2106}(215, \cdot)\) n/a 224 4
2106.2.bc \(\chi_{2106}(917, \cdot)\) n/a 224 4
2106.2.bg \(\chi_{2106}(593, \cdot)\) n/a 224 4
2106.2.bj \(\chi_{2106}(361, \cdot)\) n/a 252 6
2106.2.bk \(\chi_{2106}(181, \cdot)\) n/a 252 6
2106.2.bp \(\chi_{2106}(127, \cdot)\) n/a 252 6
2106.2.bq \(\chi_{2106}(61, \cdot)\) n/a 2268 18
2106.2.br \(\chi_{2106}(79, \cdot)\) n/a 1944 18
2106.2.bs \(\chi_{2106}(133, \cdot)\) n/a 2268 18
2106.2.bu \(\chi_{2106}(305, \cdot)\) n/a 504 12
2106.2.bv \(\chi_{2106}(125, \cdot)\) n/a 504 12
2106.2.by \(\chi_{2106}(71, \cdot)\) n/a 504 12
2106.2.bz \(\chi_{2106}(25, \cdot)\) n/a 2268 18
2106.2.ca \(\chi_{2106}(43, \cdot)\) n/a 2268 18
2106.2.cb \(\chi_{2106}(121, \cdot)\) n/a 2268 18
2106.2.cl \(\chi_{2106}(5, \cdot)\) n/a 4536 36
2106.2.cm \(\chi_{2106}(41, \cdot)\) n/a 4536 36
2106.2.cn \(\chi_{2106}(11, \cdot)\) n/a 4536 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2106))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2106)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(702))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1053))\)\(^{\oplus 2}\)