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Properties

Label 2289.1
Level 2289
Weight 1
Dimension 204
Nonzero newspaces 10
Newform subspaces 21
Sturm bound 380160
Trace bound 91

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Defining parameters

Level: \( N \) = \( 2289 = 3 \cdot 7 \cdot 109 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 21 \)
Sturm bound: \(380160\)
Trace bound: \(91\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2289))\).

Total New Old
Modular forms 2944 1276 1668
Cusp forms 352 204 148
Eisenstein series 2592 1072 1520

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 204 0 0 0

Trace form

\( 204 q - 12 q^{4} - 12 q^{9} + O(q^{10}) \) \( 204 q - 12 q^{4} - 12 q^{9} - 12 q^{16} - 12 q^{25} + 24 q^{36} + 24 q^{64} - 12 q^{81} + 12 q^{82} - 12 q^{84} + 12 q^{88} - 18 q^{91} - 36 q^{93} - 24 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2289))\)

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
2289.1.b \(\chi_{2289}(764, \cdot)\) None 0 1
2289.1.c \(\chi_{2289}(1525, \cdot)\) None 0 1
2289.1.f \(\chi_{2289}(328, \cdot)\) None 0 1
2289.1.g \(\chi_{2289}(1961, \cdot)\) None 0 1
2289.1.o \(\chi_{2289}(1450, \cdot)\) None 0 2
2289.1.p \(\chi_{2289}(251, \cdot)\) 2289.1.p.a 2 2
2289.1.p.b 2
2289.1.s \(\chi_{2289}(281, \cdot)\) None 0 2
2289.1.t \(\chi_{2289}(391, \cdot)\) None 0 2
2289.1.u \(\chi_{2289}(1136, \cdot)\) None 0 2
2289.1.v \(\chi_{2289}(808, \cdot)\) None 0 2
2289.1.y \(\chi_{2289}(809, \cdot)\) None 0 2
2289.1.z \(\chi_{2289}(481, \cdot)\) None 0 2
2289.1.ba \(\chi_{2289}(326, \cdot)\) 2289.1.ba.a 2 2
2289.1.ba.b 2
2289.1.ba.c 2
2289.1.ba.d 2
2289.1.ba.e 2
2289.1.ba.f 2
2289.1.ba.g 4
2289.1.ba.h 4
2289.1.ba.i 4
2289.1.bb \(\chi_{2289}(1636, \cdot)\) None 0 2
2289.1.bd \(\chi_{2289}(1027, \cdot)\) None 0 2
2289.1.be \(\chi_{2289}(263, \cdot)\) None 0 2
2289.1.bj \(\chi_{2289}(544, \cdot)\) None 0 2
2289.1.bk \(\chi_{2289}(1418, \cdot)\) None 0 2
2289.1.bl \(\chi_{2289}(1354, \cdot)\) None 0 2
2289.1.bm \(\chi_{2289}(590, \cdot)\) None 0 2
2289.1.bq \(\chi_{2289}(1462, \cdot)\) None 0 2
2289.1.br \(\chi_{2289}(155, \cdot)\) None 0 2
2289.1.bv \(\chi_{2289}(41, \cdot)\) 2289.1.bv.a 4 4
2289.1.bv.b 4
2289.1.bw \(\chi_{2289}(1240, \cdot)\) None 0 4
2289.1.cb \(\chi_{2289}(142, \cdot)\) None 0 4
2289.1.cc \(\chi_{2289}(185, \cdot)\) None 0 4
2289.1.cd \(\chi_{2289}(68, \cdot)\) None 0 4
2289.1.ce \(\chi_{2289}(319, \cdot)\) None 0 4
2289.1.cj \(\chi_{2289}(395, \cdot)\) None 0 4
2289.1.ck \(\chi_{2289}(226, \cdot)\) None 0 4
2289.1.cm \(\chi_{2289}(82, \cdot)\) None 0 6
2289.1.co \(\chi_{2289}(611, \cdot)\) None 0 6
2289.1.cq \(\chi_{2289}(136, \cdot)\) None 0 6
2289.1.cr \(\chi_{2289}(71, \cdot)\) None 0 6
2289.1.ct \(\chi_{2289}(790, \cdot)\) None 0 6
2289.1.cu \(\chi_{2289}(1052, \cdot)\) None 0 6
2289.1.cv \(\chi_{2289}(284, \cdot)\) None 0 6
2289.1.cx \(\chi_{2289}(34, \cdot)\) None 0 6
2289.1.cz \(\chi_{2289}(323, \cdot)\) None 0 6
2289.1.db \(\chi_{2289}(409, \cdot)\) None 0 6
2289.1.dd \(\chi_{2289}(191, \cdot)\) None 0 6
2289.1.de \(\chi_{2289}(502, \cdot)\) None 0 6
2289.1.dk \(\chi_{2289}(164, \cdot)\) None 0 12
2289.1.dm \(\chi_{2289}(310, \cdot)\) None 0 12
2289.1.dn \(\chi_{2289}(272, \cdot)\) 2289.1.dn.a 12 12
2289.1.dn.b 12
2289.1.do \(\chi_{2289}(17, \cdot)\) None 0 12
2289.1.dr \(\chi_{2289}(295, \cdot)\) None 0 12
2289.1.ds \(\chi_{2289}(163, \cdot)\) None 0 12
2289.1.dv \(\chi_{2289}(29, \cdot)\) None 0 18
2289.1.dw \(\chi_{2289}(74, \cdot)\) 2289.1.dw.a 18 18
2289.1.dx \(\chi_{2289}(137, \cdot)\) 2289.1.dx.a 18 18
2289.1.dy \(\chi_{2289}(97, \cdot)\) None 0 18
2289.1.dz \(\chi_{2289}(73, \cdot)\) None 0 18
2289.1.ec \(\chi_{2289}(124, \cdot)\) None 0 18
2289.1.eg \(\chi_{2289}(433, \cdot)\) None 0 18
2289.1.eh \(\chi_{2289}(31, \cdot)\) None 0 18
2289.1.ej \(\chi_{2289}(145, \cdot)\) None 0 18
2289.1.em \(\chi_{2289}(134, \cdot)\) None 0 18
2289.1.en \(\chi_{2289}(158, \cdot)\) 2289.1.en.a 18 18
2289.1.ep \(\chi_{2289}(116, \cdot)\) 2289.1.ep.a 18 18
2289.1.eq \(\chi_{2289}(47, \cdot)\) 2289.1.eq.a 36 36
2289.1.er \(\chi_{2289}(37, \cdot)\) None 0 36
2289.1.ew \(\chi_{2289}(59, \cdot)\) 2289.1.ew.a 36 36
2289.1.ex \(\chi_{2289}(58, \cdot)\) None 0 36
2289.1.fa \(\chi_{2289}(62, \cdot)\) None 0 36
2289.1.fb \(\chi_{2289}(85, \cdot)\) None 0 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2289))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2289)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(109))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(327))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(763))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2289))\)\(^{\oplus 1}\)