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Properties

Label 3895.1
Level 3895
Weight 1
Dimension 22
Nonzero newspaces 1
Newform subspaces 8
Sturm bound 1209600
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3895 = 5 \cdot 19 \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 8 \)
Sturm bound: \(1209600\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3895))\).

Total New Old
Modular forms 5812 4002 1810
Cusp forms 52 22 30
Eisenstein series 5760 3980 1780

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 22 0 0 0

Trace form

\( 22 q + 2 q^{4} - 4 q^{5} + 2 q^{9} + O(q^{10}) \) \( 22 q + 2 q^{4} - 4 q^{5} + 2 q^{9} + 14 q^{16} - 4 q^{20} + 12 q^{25} + 22 q^{36} - 4 q^{45} + 2 q^{49} - 8 q^{61} - 6 q^{64} - 8 q^{74} - 12 q^{80} + 22 q^{81} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3895))\)

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
3895.1.c \(\chi_{3895}(2051, \cdot)\) None 0 1
3895.1.d \(\chi_{3895}(2336, \cdot)\) None 0 1
3895.1.g \(\chi_{3895}(3894, \cdot)\) 3895.1.g.a 1 1
3895.1.g.b 1
3895.1.g.c 2
3895.1.g.d 2
3895.1.g.e 4
3895.1.g.f 4
3895.1.g.g 4
3895.1.g.h 4
3895.1.h \(\chi_{3895}(3609, \cdot)\) None 0 1
3895.1.k \(\chi_{3895}(1139, \cdot)\) None 0 2
3895.1.m \(\chi_{3895}(647, \cdot)\) None 0 2
3895.1.o \(\chi_{3895}(2623, \cdot)\) None 0 2
3895.1.p \(\chi_{3895}(2338, \cdot)\) None 0 2
3895.1.r \(\chi_{3895}(1977, \cdot)\) None 0 2
3895.1.u \(\chi_{3895}(911, \cdot)\) None 0 2
3895.1.w \(\chi_{3895}(1969, \cdot)\) None 0 2
3895.1.y \(\chi_{3895}(2254, \cdot)\) None 0 2
3895.1.z \(\chi_{3895}(696, \cdot)\) None 0 2
3895.1.bc \(\chi_{3895}(411, \cdot)\) None 0 2
3895.1.be \(\chi_{3895}(588, \cdot)\) None 0 4
3895.1.bg \(\chi_{3895}(1274, \cdot)\) None 0 4
3895.1.bh \(\chi_{3895}(96, \cdot)\) None 0 4
3895.1.bk \(\chi_{3895}(208, \cdot)\) None 0 4
3895.1.bm \(\chi_{3895}(189, \cdot)\) None 0 4
3895.1.bo \(\chi_{3895}(379, \cdot)\) None 0 4
3895.1.bp \(\chi_{3895}(816, \cdot)\) None 0 4
3895.1.bs \(\chi_{3895}(1671, \cdot)\) None 0 4
3895.1.bt \(\chi_{3895}(1836, \cdot)\) None 0 4
3895.1.bv \(\chi_{3895}(1303, \cdot)\) None 0 4
3895.1.by \(\chi_{3895}(83, \cdot)\) None 0 4
3895.1.bz \(\chi_{3895}(163, \cdot)\) None 0 4
3895.1.cc \(\chi_{3895}(2082, \cdot)\) None 0 4
3895.1.cd \(\chi_{3895}(829, \cdot)\) None 0 4
3895.1.cg \(\chi_{3895}(204, \cdot)\) None 0 6
3895.1.ch \(\chi_{3895}(1231, \cdot)\) None 0 6
3895.1.cj \(\chi_{3895}(124, \cdot)\) None 0 6
3895.1.cm \(\chi_{3895}(1516, \cdot)\) None 0 6
3895.1.cn \(\chi_{3895}(531, \cdot)\) None 0 8
3895.1.cp \(\chi_{3895}(77, \cdot)\) None 0 8
3895.1.cr \(\chi_{3895}(1103, \cdot)\) None 0 8
3895.1.cu \(\chi_{3895}(742, \cdot)\) None 0 8
3895.1.cw \(\chi_{3895}(172, \cdot)\) None 0 8
3895.1.cx \(\chi_{3895}(569, \cdot)\) None 0 8
3895.1.da \(\chi_{3895}(27, \cdot)\) None 0 8
3895.1.db \(\chi_{3895}(2709, \cdot)\) None 0 8
3895.1.de \(\chi_{3895}(1151, \cdot)\) None 0 8
3895.1.dg \(\chi_{3895}(202, \cdot)\) None 0 8
3895.1.di \(\chi_{3895}(31, \cdot)\) None 0 8
3895.1.dj \(\chi_{3895}(141, \cdot)\) None 0 8
3895.1.dl \(\chi_{3895}(734, \cdot)\) None 0 8
3895.1.dm \(\chi_{3895}(1589, \cdot)\) None 0 8
3895.1.do \(\chi_{3895}(237, \cdot)\) None 0 12
3895.1.dr \(\chi_{3895}(91, \cdot)\) None 0 12
3895.1.ds \(\chi_{3895}(42, \cdot)\) None 0 12
3895.1.du \(\chi_{3895}(327, \cdot)\) None 0 12
3895.1.dx \(\chi_{3895}(319, \cdot)\) None 0 12
3895.1.dz \(\chi_{3895}(73, \cdot)\) None 0 12
3895.1.ea \(\chi_{3895}(227, \cdot)\) None 0 16
3895.1.ed \(\chi_{3895}(381, \cdot)\) None 0 16
3895.1.ee \(\chi_{3895}(134, \cdot)\) None 0 16
3895.1.eg \(\chi_{3895}(417, \cdot)\) None 0 16
3895.1.ek \(\chi_{3895}(84, \cdot)\) None 0 16
3895.1.em \(\chi_{3895}(87, \cdot)\) None 0 16
3895.1.en \(\chi_{3895}(277, \cdot)\) None 0 16
3895.1.eq \(\chi_{3895}(182, \cdot)\) None 0 16
3895.1.er \(\chi_{3895}(102, \cdot)\) None 0 16
3895.1.eu \(\chi_{3895}(46, \cdot)\) None 0 16
3895.1.ev \(\chi_{3895}(3, \cdot)\) None 0 24
3895.1.ey \(\chi_{3895}(44, \cdot)\) None 0 24
3895.1.fa \(\chi_{3895}(161, \cdot)\) None 0 24
3895.1.fb \(\chi_{3895}(167, \cdot)\) None 0 24
3895.1.fd \(\chi_{3895}(86, \cdot)\) None 0 24
3895.1.fg \(\chi_{3895}(59, \cdot)\) None 0 24
3895.1.fi \(\chi_{3895}(51, \cdot)\) None 0 24
3895.1.fj \(\chi_{3895}(154, \cdot)\) None 0 24
3895.1.fk \(\chi_{3895}(12, \cdot)\) None 0 32
3895.1.fm \(\chi_{3895}(11, \cdot)\) None 0 32
3895.1.fp \(\chi_{3895}(239, \cdot)\) None 0 32
3895.1.fq \(\chi_{3895}(198, \cdot)\) None 0 32
3895.1.fs \(\chi_{3895}(43, \cdot)\) None 0 48
3895.1.fu \(\chi_{3895}(184, \cdot)\) None 0 48
3895.1.fx \(\chi_{3895}(23, \cdot)\) None 0 48
3895.1.fz \(\chi_{3895}(92, \cdot)\) None 0 48
3895.1.ga \(\chi_{3895}(21, \cdot)\) None 0 48
3895.1.gd \(\chi_{3895}(207, \cdot)\) None 0 48
3895.1.gf \(\chi_{3895}(52, \cdot)\) None 0 96
3895.1.gg \(\chi_{3895}(6, \cdot)\) None 0 96
3895.1.gi \(\chi_{3895}(24, \cdot)\) None 0 96
3895.1.gl \(\chi_{3895}(13, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3895))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3895)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(779))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3895))\)\(^{\oplus 1}\)