Properties

Label 4017.2
Level 4017
Weight 2
Dimension 437931
Nonzero newspaces 60
Sturm bound 2376192

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Defining parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(2376192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4017))\).

Total New Old
Modular forms 598944 442371 156573
Cusp forms 589153 437931 151222
Eisenstein series 9791 4440 5351

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4017))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4017.2.a \(\chi_{4017}(1, \cdot)\) 4017.2.a.a 1 1
4017.2.a.b 1
4017.2.a.c 1
4017.2.a.d 2
4017.2.a.e 16
4017.2.a.f 19
4017.2.a.g 24
4017.2.a.h 25
4017.2.a.i 25
4017.2.a.j 25
4017.2.a.k 32
4017.2.a.l 32
4017.2.b \(\chi_{4017}(1546, \cdot)\) n/a 240 1
4017.2.e \(\chi_{4017}(2471, \cdot)\) n/a 416 1
4017.2.f \(\chi_{4017}(4016, \cdot)\) n/a 480 1
4017.2.i \(\chi_{4017}(880, \cdot)\) n/a 486 2
4017.2.j \(\chi_{4017}(664, \cdot)\) n/a 416 2
4017.2.k \(\chi_{4017}(1855, \cdot)\) n/a 472 2
4017.2.l \(\chi_{4017}(1498, \cdot)\) n/a 486 2
4017.2.m \(\chi_{4017}(1958, \cdot)\) n/a 952 2
4017.2.p \(\chi_{4017}(1750, \cdot)\) n/a 488 2
4017.2.r \(\chi_{4017}(1901, \cdot)\) n/a 962 2
4017.2.s \(\chi_{4017}(355, \cdot)\) n/a 486 2
4017.2.v \(\chi_{4017}(1544, \cdot)\) n/a 964 2
4017.2.ba \(\chi_{4017}(974, \cdot)\) n/a 964 2
4017.2.bb \(\chi_{4017}(881, \cdot)\) n/a 962 2
4017.2.be \(\chi_{4017}(3091, \cdot)\) n/a 480 2
4017.2.bf \(\chi_{4017}(1808, \cdot)\) n/a 832 2
4017.2.bg \(\chi_{4017}(263, \cdot)\) n/a 962 2
4017.2.bl \(\chi_{4017}(2734, \cdot)\) n/a 486 2
4017.2.bm \(\chi_{4017}(571, \cdot)\) n/a 484 2
4017.2.bn \(\chi_{4017}(308, \cdot)\) n/a 964 2
4017.2.bq \(\chi_{4017}(1499, \cdot)\) n/a 962 2
4017.2.bt \(\chi_{4017}(2416, \cdot)\) n/a 972 4
4017.2.bu \(\chi_{4017}(149, \cdot)\) n/a 1924 4
4017.2.bw \(\chi_{4017}(983, \cdot)\) n/a 1928 4
4017.2.ca \(\chi_{4017}(514, \cdot)\) n/a 968 4
4017.2.cb \(\chi_{4017}(253, \cdot)\) n/a 972 4
4017.2.cc \(\chi_{4017}(722, \cdot)\) n/a 1904 4
4017.2.cd \(\chi_{4017}(2312, \cdot)\) n/a 1924 4
4017.2.ch \(\chi_{4017}(1087, \cdot)\) n/a 968 4
4017.2.ci \(\chi_{4017}(79, \cdot)\) n/a 3328 16
4017.2.cl \(\chi_{4017}(233, \cdot)\) n/a 7680 16
4017.2.cm \(\chi_{4017}(209, \cdot)\) n/a 6656 16
4017.2.cp \(\chi_{4017}(64, \cdot)\) n/a 3904 16
4017.2.cq \(\chi_{4017}(334, \cdot)\) n/a 7776 32
4017.2.cr \(\chi_{4017}(61, \cdot)\) n/a 7744 32
4017.2.cs \(\chi_{4017}(118, \cdot)\) n/a 6656 32
4017.2.ct \(\chi_{4017}(16, \cdot)\) n/a 7776 32
4017.2.cu \(\chi_{4017}(31, \cdot)\) n/a 7808 32
4017.2.cx \(\chi_{4017}(8, \cdot)\) n/a 15360 32
4017.2.cz \(\chi_{4017}(212, \cdot)\) n/a 15392 32
4017.2.dc \(\chi_{4017}(113, \cdot)\) n/a 15424 32
4017.2.dd \(\chi_{4017}(25, \cdot)\) n/a 7744 32
4017.2.de \(\chi_{4017}(4, \cdot)\) n/a 7776 32
4017.2.dj \(\chi_{4017}(146, \cdot)\) n/a 15392 32
4017.2.dk \(\chi_{4017}(53, \cdot)\) n/a 13312 32
4017.2.dl \(\chi_{4017}(322, \cdot)\) n/a 7744 32
4017.2.do \(\chi_{4017}(62, \cdot)\) n/a 15392 32
4017.2.dp \(\chi_{4017}(77, \cdot)\) n/a 15424 32
4017.2.du \(\chi_{4017}(95, \cdot)\) n/a 15424 32
4017.2.dx \(\chi_{4017}(121, \cdot)\) n/a 7776 32
4017.2.dy \(\chi_{4017}(35, \cdot)\) n/a 15392 32
4017.2.ea \(\chi_{4017}(70, \cdot)\) n/a 15488 64
4017.2.ee \(\chi_{4017}(2, \cdot)\) n/a 30784 64
4017.2.ef \(\chi_{4017}(137, \cdot)\) n/a 30848 64
4017.2.eg \(\chi_{4017}(124, \cdot)\) n/a 15552 64
4017.2.eh \(\chi_{4017}(37, \cdot)\) n/a 15488 64
4017.2.el \(\chi_{4017}(83, \cdot)\) n/a 30848 64
4017.2.en \(\chi_{4017}(50, \cdot)\) n/a 30784 64
4017.2.eo \(\chi_{4017}(67, \cdot)\) n/a 15552 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4017))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4017)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(309))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1339))\)\(^{\oplus 2}\)