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Properties

Label 2112.2
Level 2112
Weight 2
Dimension 50580
Nonzero newspaces 32
Sturm bound 491520
Trace bound 33

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Defining parameters

Level: \( N \) = \( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(491520\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2112))\).

Total New Old
Modular forms 125760 51372 74388
Cusp forms 120001 50580 69421
Eisenstein series 5759 792 4967

Trace form

\( 50580 q - 48 q^{3} - 128 q^{4} - 64 q^{6} - 104 q^{7} - 80 q^{9} + O(q^{10}) \) \( 50580 q - 48 q^{3} - 128 q^{4} - 64 q^{6} - 104 q^{7} - 80 q^{9} - 128 q^{10} - 8 q^{11} - 144 q^{12} - 160 q^{13} - 60 q^{15} - 128 q^{16} - 32 q^{17} - 64 q^{18} - 128 q^{19} - 56 q^{21} - 128 q^{22} + 16 q^{24} - 116 q^{25} + 160 q^{26} - 24 q^{27} + 32 q^{28} + 64 q^{29} + 96 q^{30} - 8 q^{31} + 160 q^{32} - 16 q^{33} - 128 q^{34} + 48 q^{35} + 96 q^{36} - 64 q^{37} + 160 q^{38} - 4 q^{39} + 32 q^{40} + 64 q^{41} + 16 q^{42} - 80 q^{43} + 16 q^{44} - 56 q^{45} - 128 q^{46} - 64 q^{48} - 196 q^{49} - 96 q^{50} + 84 q^{51} - 320 q^{52} - 96 q^{54} + 48 q^{55} - 224 q^{56} - 28 q^{57} - 416 q^{58} + 320 q^{59} - 256 q^{60} - 128 q^{61} - 192 q^{62} + 20 q^{63} - 512 q^{64} + 32 q^{65} - 152 q^{66} + 136 q^{67} - 192 q^{68} - 136 q^{69} - 512 q^{70} + 256 q^{71} - 64 q^{72} - 160 q^{73} - 224 q^{74} + 48 q^{75} - 384 q^{76} - 48 q^{77} - 288 q^{78} - 8 q^{79} - 96 q^{80} - 240 q^{81} - 128 q^{82} - 80 q^{83} - 288 q^{84} - 224 q^{85} - 144 q^{87} - 144 q^{88} - 64 q^{89} - 352 q^{90} - 216 q^{91} - 176 q^{93} - 128 q^{94} - 96 q^{95} - 336 q^{96} - 192 q^{97} - 112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2112))\)

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
2112.2.a \(\chi_{2112}(1, \cdot)\) 2112.2.a.a 1 1
2112.2.a.b 1
2112.2.a.c 1
2112.2.a.d 1
2112.2.a.e 1
2112.2.a.f 1
2112.2.a.g 1
2112.2.a.h 1
2112.2.a.i 1
2112.2.a.j 1
2112.2.a.k 1
2112.2.a.l 1
2112.2.a.m 1
2112.2.a.n 1
2112.2.a.o 1
2112.2.a.p 1
2112.2.a.q 1
2112.2.a.r 1
2112.2.a.s 1
2112.2.a.t 1
2112.2.a.u 1
2112.2.a.v 1
2112.2.a.w 1
2112.2.a.x 1
2112.2.a.y 1
2112.2.a.z 1
2112.2.a.ba 1
2112.2.a.bb 1
2112.2.a.bc 1
2112.2.a.bd 1
2112.2.a.be 2
2112.2.a.bf 2
2112.2.a.bg 3
2112.2.a.bh 3
2112.2.b \(\chi_{2112}(65, \cdot)\) 2112.2.b.a 2 1
2112.2.b.b 2
2112.2.b.c 2
2112.2.b.d 2
2112.2.b.e 2
2112.2.b.f 2
2112.2.b.g 2
2112.2.b.h 2
2112.2.b.i 2
2112.2.b.j 2
2112.2.b.k 4
2112.2.b.l 4
2112.2.b.m 4
2112.2.b.n 4
2112.2.b.o 6
2112.2.b.p 6
2112.2.b.q 6
2112.2.b.r 6
2112.2.b.s 8
2112.2.b.t 8
2112.2.b.u 8
2112.2.b.v 8
2112.2.d \(\chi_{2112}(1343, \cdot)\) 2112.2.d.a 2 1
2112.2.d.b 2
2112.2.d.c 2
2112.2.d.d 2
2112.2.d.e 2
2112.2.d.f 2
2112.2.d.g 2
2112.2.d.h 2
2112.2.d.i 4
2112.2.d.j 4
2112.2.d.k 8
2112.2.d.l 8
2112.2.d.m 20
2112.2.d.n 20
2112.2.f \(\chi_{2112}(1057, \cdot)\) 2112.2.f.a 4 1
2112.2.f.b 4
2112.2.f.c 4
2112.2.f.d 4
2112.2.f.e 4
2112.2.f.f 4
2112.2.f.g 8
2112.2.f.h 8
2112.2.h \(\chi_{2112}(1759, \cdot)\) 2112.2.h.a 8 1
2112.2.h.b 8
2112.2.h.c 16
2112.2.h.d 16
2112.2.k \(\chi_{2112}(287, \cdot)\) 2112.2.k.a 4 1
2112.2.k.b 4
2112.2.k.c 4
2112.2.k.d 4
2112.2.k.e 4
2112.2.k.f 4
2112.2.k.g 4
2112.2.k.h 4
2112.2.k.i 8
2112.2.k.j 8
2112.2.k.k 16
2112.2.k.l 16
2112.2.m \(\chi_{2112}(1121, \cdot)\) 2112.2.m.a 4 1
2112.2.m.b 4
2112.2.m.c 4
2112.2.m.d 4
2112.2.m.e 8
2112.2.m.f 8
2112.2.m.g 8
2112.2.m.h 8
2112.2.m.i 8
2112.2.m.j 8
2112.2.m.k 8
2112.2.m.l 8
2112.2.m.m 16
2112.2.o \(\chi_{2112}(703, \cdot)\) 2112.2.o.a 4 1
2112.2.o.b 4
2112.2.o.c 4
2112.2.o.d 4
2112.2.o.e 8
2112.2.o.f 12
2112.2.o.g 12
2112.2.q \(\chi_{2112}(175, \cdot)\) 2112.2.q.a 96 2
2112.2.t \(\chi_{2112}(529, \cdot)\) 2112.2.t.a 40 2
2112.2.t.b 40
2112.2.u \(\chi_{2112}(815, \cdot)\) n/a 160 2
2112.2.x \(\chi_{2112}(593, \cdot)\) n/a 184 2
2112.2.y \(\chi_{2112}(577, \cdot)\) n/a 192 4
2112.2.bb \(\chi_{2112}(265, \cdot)\) None 0 4
2112.2.bc \(\chi_{2112}(329, \cdot)\) None 0 4
2112.2.bd \(\chi_{2112}(23, \cdot)\) None 0 4
2112.2.be \(\chi_{2112}(439, \cdot)\) None 0 4
2112.2.bi \(\chi_{2112}(127, \cdot)\) n/a 192 4
2112.2.bk \(\chi_{2112}(161, \cdot)\) n/a 384 4
2112.2.bm \(\chi_{2112}(863, \cdot)\) n/a 384 4
2112.2.bp \(\chi_{2112}(415, \cdot)\) n/a 192 4
2112.2.br \(\chi_{2112}(97, \cdot)\) n/a 192 4
2112.2.bt \(\chi_{2112}(191, \cdot)\) n/a 368 4
2112.2.bv \(\chi_{2112}(833, \cdot)\) n/a 368 4
2112.2.by \(\chi_{2112}(197, \cdot)\) n/a 3040 8
2112.2.bz \(\chi_{2112}(133, \cdot)\) n/a 1280 8
2112.2.ca \(\chi_{2112}(155, \cdot)\) n/a 2560 8
2112.2.cb \(\chi_{2112}(43, \cdot)\) n/a 1536 8
2112.2.ce \(\chi_{2112}(17, \cdot)\) n/a 736 8
2112.2.ch \(\chi_{2112}(47, \cdot)\) n/a 736 8
2112.2.ci \(\chi_{2112}(49, \cdot)\) n/a 384 8
2112.2.cl \(\chi_{2112}(79, \cdot)\) n/a 384 8
2112.2.co \(\chi_{2112}(7, \cdot)\) None 0 16
2112.2.cp \(\chi_{2112}(71, \cdot)\) None 0 16
2112.2.cq \(\chi_{2112}(41, \cdot)\) None 0 16
2112.2.cr \(\chi_{2112}(25, \cdot)\) None 0 16
2112.2.cu \(\chi_{2112}(19, \cdot)\) n/a 6144 32
2112.2.cv \(\chi_{2112}(59, \cdot)\) n/a 12160 32
2112.2.da \(\chi_{2112}(37, \cdot)\) n/a 6144 32
2112.2.db \(\chi_{2112}(29, \cdot)\) n/a 12160 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2112))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2112)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1056))\)\(^{\oplus 2}\)