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Properties

Label 1911.1
Level 1911
Weight 1
Dimension 229
Nonzero newspaces 20
Newform subspaces 39
Sturm bound 263424
Trace bound 37

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Defining parameters

Level: \( N \) = \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 39 \)
Sturm bound: \(263424\)
Trace bound: \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1911))\).

Total New Old
Modular forms 3180 1295 1885
Cusp forms 300 229 71
Eisenstein series 2880 1066 1814

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 213 16 0 0

Trace form

\( 229 q + 3 q^{3} + 3 q^{4} + 4 q^{6} + 2 q^{7} + 7 q^{9} + O(q^{10}) \) \( 229 q + 3 q^{3} + 3 q^{4} + 4 q^{6} + 2 q^{7} + 7 q^{9} + 2 q^{10} + 5 q^{12} + 11 q^{13} - 8 q^{15} + 7 q^{16} + 8 q^{19} + 2 q^{21} - 24 q^{22} - 2 q^{24} + 3 q^{25} + 3 q^{27} + 2 q^{28} + 4 q^{31} - 8 q^{34} + 33 q^{36} - 8 q^{37} - 2 q^{39} - 4 q^{40} - 34 q^{43} - 2 q^{46} - 11 q^{48} + 2 q^{49} - 4 q^{51} - 2 q^{52} + 2 q^{54} - 4 q^{57} - 2 q^{58} - 8 q^{61} - 12 q^{63} - 7 q^{64} + 8 q^{67} - 4 q^{69} - 12 q^{73} - 19 q^{75} - 16 q^{76} + 8 q^{78} + 10 q^{79} - 21 q^{81} + 2 q^{82} - 10 q^{84} - 8 q^{85} + 2 q^{87} - 8 q^{90} - 10 q^{91} - 16 q^{93} + 2 q^{94} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1911))\)

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
1911.1.b \(\chi_{1911}(638, \cdot)\) None 0 1
1911.1.d \(\chi_{1911}(1273, \cdot)\) None 0 1
1911.1.f \(\chi_{1911}(391, \cdot)\) None 0 1
1911.1.h \(\chi_{1911}(1520, \cdot)\) 1911.1.h.a 1 1
1911.1.h.b 2
1911.1.h.c 2
1911.1.h.d 4
1911.1.h.e 4
1911.1.m \(\chi_{1911}(148, \cdot)\) None 0 2
1911.1.o \(\chi_{1911}(1175, \cdot)\) None 0 2
1911.1.q \(\chi_{1911}(166, \cdot)\) None 0 2
1911.1.s \(\chi_{1911}(1439, \cdot)\) 1911.1.s.a 2 2
1911.1.s.b 4
1911.1.v \(\chi_{1911}(685, \cdot)\) None 0 2
1911.1.w \(\chi_{1911}(116, \cdot)\) 1911.1.w.a 2 2
1911.1.w.b 2
1911.1.w.c 4
1911.1.w.d 4
1911.1.w.e 8
1911.1.w.f 8
1911.1.x \(\chi_{1911}(998, \cdot)\) 1911.1.x.a 2 2
1911.1.z \(\chi_{1911}(607, \cdot)\) None 0 2
1911.1.bb \(\chi_{1911}(313, \cdot)\) None 0 2
1911.1.bc \(\chi_{1911}(491, \cdot)\) 1911.1.bc.a 2 2
1911.1.bc.b 2
1911.1.be \(\chi_{1911}(932, \cdot)\) 1911.1.be.a 2 2
1911.1.be.b 2
1911.1.be.c 4
1911.1.be.d 4
1911.1.bg \(\chi_{1911}(901, \cdot)\) None 0 2
1911.1.bi \(\chi_{1911}(766, \cdot)\) None 0 2
1911.1.bk \(\chi_{1911}(716, \cdot)\) None 0 2
1911.1.bm \(\chi_{1911}(263, \cdot)\) 1911.1.bm.a 2 2
1911.1.bm.b 4
1911.1.bo \(\chi_{1911}(244, \cdot)\) None 0 2
1911.1.bp \(\chi_{1911}(569, \cdot)\) 1911.1.bp.a 2 2
1911.1.bq \(\chi_{1911}(178, \cdot)\) None 0 2
1911.1.bt \(\chi_{1911}(227, \cdot)\) 1911.1.bt.a 4 4
1911.1.bv \(\chi_{1911}(214, \cdot)\) None 0 4
1911.1.by \(\chi_{1911}(67, \cdot)\) None 0 4
1911.1.cb \(\chi_{1911}(293, \cdot)\) 1911.1.cb.a 4 4
1911.1.cb.b 4
1911.1.cc \(\chi_{1911}(668, \cdot)\) 1911.1.cc.a 4 4
1911.1.cc.b 4
1911.1.cf \(\chi_{1911}(1177, \cdot)\) None 0 4
1911.1.cg \(\chi_{1911}(226, \cdot)\) None 0 4
1911.1.ci \(\chi_{1911}(80, \cdot)\) 1911.1.ci.a 4 4
1911.1.cj \(\chi_{1911}(155, \cdot)\) 1911.1.cj.a 6 6
1911.1.cj.b 6
1911.1.cl \(\chi_{1911}(118, \cdot)\) None 0 6
1911.1.cn \(\chi_{1911}(181, \cdot)\) None 0 6
1911.1.cp \(\chi_{1911}(92, \cdot)\) None 0 6
1911.1.cv \(\chi_{1911}(83, \cdot)\) 1911.1.cv.a 12 12
1911.1.cv.b 12
1911.1.cx \(\chi_{1911}(190, \cdot)\) None 0 12
1911.1.cz \(\chi_{1911}(250, \cdot)\) None 0 12
1911.1.da \(\chi_{1911}(23, \cdot)\) 1911.1.da.a 12 12
1911.1.db \(\chi_{1911}(160, \cdot)\) None 0 12
1911.1.dd \(\chi_{1911}(191, \cdot)\) 1911.1.dd.a 12 12
1911.1.df \(\chi_{1911}(53, \cdot)\) None 0 12
1911.1.dh \(\chi_{1911}(103, \cdot)\) None 0 12
1911.1.dj \(\chi_{1911}(10, \cdot)\) None 0 12
1911.1.dl \(\chi_{1911}(29, \cdot)\) None 0 12
1911.1.dn \(\chi_{1911}(134, \cdot)\) None 0 12
1911.1.do \(\chi_{1911}(40, \cdot)\) None 0 12
1911.1.dq \(\chi_{1911}(61, \cdot)\) None 0 12
1911.1.ds \(\chi_{1911}(179, \cdot)\) 1911.1.ds.a 12 12
1911.1.dt \(\chi_{1911}(233, \cdot)\) None 0 12
1911.1.du \(\chi_{1911}(55, \cdot)\) None 0 12
1911.1.dx \(\chi_{1911}(74, \cdot)\) 1911.1.dx.a 12 12
1911.1.dz \(\chi_{1911}(199, \cdot)\) None 0 12
1911.1.ea \(\chi_{1911}(110, \cdot)\) 1911.1.ea.a 24 24
1911.1.ec \(\chi_{1911}(109, \cdot)\) None 0 24
1911.1.ed \(\chi_{1911}(85, \cdot)\) None 0 24
1911.1.eg \(\chi_{1911}(5, \cdot)\) None 0 24
1911.1.eh \(\chi_{1911}(20, \cdot)\) None 0 24
1911.1.ek \(\chi_{1911}(58, \cdot)\) None 0 24
1911.1.en \(\chi_{1911}(37, \cdot)\) None 0 24
1911.1.ep \(\chi_{1911}(59, \cdot)\) 1911.1.ep.a 24 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1911))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1911)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 2}\)