Properties

Label 2548.1
Level 2548
Weight 1
Dimension 190
Nonzero newspaces 18
Newform subspaces 32
Sturm bound 395136
Trace bound 50

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Defining parameters

Level: \( N \) = \( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 32 \)
Sturm bound: \(395136\)
Trace bound: \(50\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2548))\).

Total New Old
Modular forms 3814 1256 2558
Cusp forms 214 190 24
Eisenstein series 3600 1066 2534

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 178 0 12 0

Trace form

\( 190 q + q^{2} + 3 q^{4} + 2 q^{5} - 2 q^{8} + q^{9} + O(q^{10}) \) \( 190 q + q^{2} + 3 q^{4} + 2 q^{5} - 2 q^{8} + q^{9} - q^{10} - 9 q^{13} + 12 q^{15} + 3 q^{16} - 9 q^{17} - 2 q^{18} - q^{20} - 8 q^{22} + 2 q^{23} + 2 q^{25} + q^{26} - 25 q^{29} + q^{32} + 2 q^{34} - 9 q^{36} - q^{37} + 34 q^{38} + 2 q^{40} - q^{41} - 4 q^{43} - q^{45} - 24 q^{50} - 4 q^{53} + 12 q^{57} - q^{58} - 9 q^{61} + 22 q^{62} - 12 q^{64} + q^{65} - 9 q^{68} - 12 q^{71} + q^{72} + 2 q^{73} - q^{74} + 2 q^{79} - q^{80} + q^{81} - q^{82} - 35 q^{85} - 8 q^{88} + 2 q^{89} + 2 q^{90} - 8 q^{94} - 2 q^{95} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2548))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2548.1.b \(\chi_{2548}(1665, \cdot)\) None 0 1
2548.1.c \(\chi_{2548}(883, \cdot)\) 2548.1.c.a 1 1
2548.1.c.b 1
2548.1.c.c 1
2548.1.c.d 1
2548.1.c.e 4
2548.1.d \(\chi_{2548}(1273, \cdot)\) None 0 1
2548.1.e \(\chi_{2548}(1275, \cdot)\) None 0 1
2548.1.o \(\chi_{2548}(785, \cdot)\) 2548.1.o.a 4 2
2548.1.p \(\chi_{2548}(1175, \cdot)\) 2548.1.p.a 8 2
2548.1.q \(\chi_{2548}(263, \cdot)\) 2548.1.q.a 2 2
2548.1.q.b 2
2548.1.q.c 4
2548.1.r \(\chi_{2548}(901, \cdot)\) None 0 2
2548.1.s \(\chi_{2548}(667, \cdot)\) 2548.1.s.a 8 2
2548.1.t \(\chi_{2548}(913, \cdot)\) None 0 2
2548.1.bd \(\chi_{2548}(491, \cdot)\) 2548.1.bd.a 8 2
2548.1.be \(\chi_{2548}(685, \cdot)\) None 0 2
2548.1.bf \(\chi_{2548}(79, \cdot)\) None 0 2
2548.1.bg \(\chi_{2548}(129, \cdot)\) 2548.1.bg.a 2 2
2548.1.bg.b 2
2548.1.bh \(\chi_{2548}(1109, \cdot)\) None 0 2
2548.1.bi \(\chi_{2548}(471, \cdot)\) 2548.1.bi.a 2 2
2548.1.bi.b 2
2548.1.bi.c 4
2548.1.bj \(\chi_{2548}(705, \cdot)\) None 0 2
2548.1.bk \(\chi_{2548}(459, \cdot)\) 2548.1.bk.a 8 2
2548.1.bl \(\chi_{2548}(2027, \cdot)\) 2548.1.bl.a 2 2
2548.1.bl.b 2
2548.1.bl.c 8
2548.1.bm \(\chi_{2548}(313, \cdot)\) None 0 2
2548.1.bn \(\chi_{2548}(295, \cdot)\) 2548.1.bn.a 2 2
2548.1.bn.b 4
2548.1.bo \(\chi_{2548}(881, \cdot)\) None 0 2
2548.1.bv \(\chi_{2548}(765, \cdot)\) None 0 4
2548.1.bw \(\chi_{2548}(587, \cdot)\) 2548.1.bw.a 16 4
2548.1.bx \(\chi_{2548}(31, \cdot)\) 2548.1.bx.a 16 4
2548.1.by \(\chi_{2548}(197, \cdot)\) None 0 4
2548.1.bz \(\chi_{2548}(177, \cdot)\) 2548.1.bz.a 8 4
2548.1.ca \(\chi_{2548}(227, \cdot)\) 2548.1.ca.a 16 4
2548.1.ch \(\chi_{2548}(19, \cdot)\) 2548.1.ch.a 16 4
2548.1.ci \(\chi_{2548}(557, \cdot)\) None 0 4
2548.1.cm \(\chi_{2548}(183, \cdot)\) None 0 6
2548.1.cn \(\chi_{2548}(181, \cdot)\) None 0 6
2548.1.co \(\chi_{2548}(155, \cdot)\) 2548.1.co.a 6 6
2548.1.co.b 6
2548.1.cp \(\chi_{2548}(209, \cdot)\) None 0 6
2548.1.cu \(\chi_{2548}(83, \cdot)\) None 0 12
2548.1.cv \(\chi_{2548}(57, \cdot)\) None 0 12
2548.1.db \(\chi_{2548}(69, \cdot)\) None 0 12
2548.1.dc \(\chi_{2548}(211, \cdot)\) None 0 12
2548.1.dd \(\chi_{2548}(157, \cdot)\) None 0 12
2548.1.de \(\chi_{2548}(51, \cdot)\) 2548.1.de.a 12 12
2548.1.de.b 12
2548.1.df \(\chi_{2548}(23, \cdot)\) None 0 12
2548.1.dg \(\chi_{2548}(269, \cdot)\) None 0 12
2548.1.dh \(\chi_{2548}(107, \cdot)\) None 0 12
2548.1.di \(\chi_{2548}(17, \cdot)\) None 0 12
2548.1.dj \(\chi_{2548}(285, \cdot)\) None 0 12
2548.1.dk \(\chi_{2548}(235, \cdot)\) None 0 12
2548.1.dl \(\chi_{2548}(237, \cdot)\) None 0 12
2548.1.dm \(\chi_{2548}(43, \cdot)\) None 0 12
2548.1.dw \(\chi_{2548}(61, \cdot)\) None 0 12
2548.1.dx \(\chi_{2548}(179, \cdot)\) None 0 12
2548.1.dy \(\chi_{2548}(101, \cdot)\) None 0 12
2548.1.dz \(\chi_{2548}(191, \cdot)\) None 0 12
2548.1.ea \(\chi_{2548}(149, \cdot)\) None 0 24
2548.1.eb \(\chi_{2548}(115, \cdot)\) None 0 24
2548.1.ei \(\chi_{2548}(59, \cdot)\) None 0 24
2548.1.ej \(\chi_{2548}(109, \cdot)\) None 0 24
2548.1.ek \(\chi_{2548}(85, \cdot)\) None 0 24
2548.1.el \(\chi_{2548}(47, \cdot)\) None 0 24
2548.1.em \(\chi_{2548}(111, \cdot)\) None 0 24
2548.1.en \(\chi_{2548}(37, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2548))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2548)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 2}\)