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Properties

Label 2496.1
Level 2496
Weight 1
Dimension 126
Nonzero newspaces 12
Newform subspaces 30
Sturm bound 344064
Trace bound 25

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Defining parameters

Level: \( N \) = \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 30 \)
Sturm bound: \(344064\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2496))\).

Total New Old
Modular forms 3900 610 3290
Cusp forms 444 126 318
Eisenstein series 3456 484 2972

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 118 0 8 0

Trace form

\( 126 q + 2 q^{9} + 2 q^{13} - 4 q^{21} - 10 q^{25} - 4 q^{33} + 8 q^{37} + 8 q^{43} - 4 q^{45} - 18 q^{49} - 32 q^{55} - 12 q^{57} + 8 q^{61} - 8 q^{69} - 4 q^{73} - 40 q^{75} - 10 q^{81} + 4 q^{85} + 8 q^{93}+ \cdots + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2496))\)

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
2496.1.b \(\chi_{2496}(545, \cdot)\) 2496.1.b.a 2 1
2496.1.b.b 2
2496.1.b.c 4
2496.1.b.d 4
2496.1.e \(\chi_{2496}(1951, \cdot)\) None 0 1
2496.1.f \(\chi_{2496}(833, \cdot)\) None 0 1
2496.1.i \(\chi_{2496}(1663, \cdot)\) None 0 1
2496.1.k \(\chi_{2496}(703, \cdot)\) None 0 1
2496.1.l \(\chi_{2496}(1793, \cdot)\) 2496.1.l.a 1 1
2496.1.l.b 1
2496.1.l.c 4
2496.1.o \(\chi_{2496}(415, \cdot)\) None 0 1
2496.1.p \(\chi_{2496}(2081, \cdot)\) None 0 1
2496.1.s \(\chi_{2496}(47, \cdot)\) None 0 2
2496.1.t \(\chi_{2496}(1009, \cdot)\) None 0 2
2496.1.w \(\chi_{2496}(209, \cdot)\) None 0 2
2496.1.y \(\chi_{2496}(1039, \cdot)\) None 0 2
2496.1.z \(\chi_{2496}(1633, \cdot)\) None 0 2
2496.1.ba \(\chi_{2496}(385, \cdot)\) None 0 2
2496.1.bd \(\chi_{2496}(1919, \cdot)\) 2496.1.bd.a 2 2
2496.1.bd.b 2
2496.1.be \(\chi_{2496}(671, \cdot)\) 2496.1.be.a 2 2
2496.1.be.b 2
2496.1.be.c 2
2496.1.be.d 2
2496.1.bi \(\chi_{2496}(1169, \cdot)\) 2496.1.bi.a 8 2
2496.1.bk \(\chi_{2496}(79, \cdot)\) None 0 2
2496.1.bl \(\chi_{2496}(1201, \cdot)\) None 0 2
2496.1.bo \(\chi_{2496}(239, \cdot)\) None 0 2
2496.1.bp \(\chi_{2496}(127, \cdot)\) None 0 2
2496.1.bs \(\chi_{2496}(1985, \cdot)\) 2496.1.bs.a 2 2
2496.1.bs.b 2
2496.1.bs.c 8
2496.1.bt \(\chi_{2496}(607, \cdot)\) None 0 2
2496.1.bw \(\chi_{2496}(1505, \cdot)\) 2496.1.bw.a 4 2
2496.1.bw.b 4
2496.1.bx \(\chi_{2496}(737, \cdot)\) 2496.1.bx.a 4 2
2496.1.bx.b 4
2496.1.by \(\chi_{2496}(1375, \cdot)\) None 0 2
2496.1.cb \(\chi_{2496}(257, \cdot)\) 2496.1.cb.a 2 2
2496.1.cb.b 2
2496.1.cc \(\chi_{2496}(1855, \cdot)\) None 0 2
2496.1.ce \(\chi_{2496}(359, \cdot)\) None 0 4
2496.1.cg \(\chi_{2496}(73, \cdot)\) None 0 4
2496.1.cj \(\chi_{2496}(391, \cdot)\) None 0 4
2496.1.cl \(\chi_{2496}(103, \cdot)\) None 0 4
2496.1.cm \(\chi_{2496}(233, \cdot)\) None 0 4
2496.1.co \(\chi_{2496}(521, \cdot)\) None 0 4
2496.1.cr \(\chi_{2496}(551, \cdot)\) None 0 4
2496.1.ct \(\chi_{2496}(265, \cdot)\) None 0 4
2496.1.cv \(\chi_{2496}(145, \cdot)\) None 0 4
2496.1.cw \(\chi_{2496}(1679, \cdot)\) None 0 4
2496.1.cy \(\chi_{2496}(367, \cdot)\) None 0 4
2496.1.da \(\chi_{2496}(17, \cdot)\) None 0 4
2496.1.de \(\chi_{2496}(479, \cdot)\) 2496.1.de.a 4 4
2496.1.de.b 4
2496.1.de.c 4
2496.1.de.d 4
2496.1.df \(\chi_{2496}(383, \cdot)\) 2496.1.df.a 4 4
2496.1.df.b 4
2496.1.di \(\chi_{2496}(193, \cdot)\) None 0 4
2496.1.dj \(\chi_{2496}(97, \cdot)\) None 0 4
2496.1.dk \(\chi_{2496}(751, \cdot)\) None 0 4
2496.1.dm \(\chi_{2496}(113, \cdot)\) None 0 4
2496.1.do \(\chi_{2496}(431, \cdot)\) None 0 4
2496.1.dr \(\chi_{2496}(1393, \cdot)\) None 0 4
2496.1.du \(\chi_{2496}(53, \cdot)\) None 0 8
2496.1.dv \(\chi_{2496}(259, \cdot)\) None 0 8
2496.1.dy \(\chi_{2496}(109, \cdot)\) None 0 8
2496.1.dz \(\chi_{2496}(83, \cdot)\) None 0 8
2496.1.ec \(\chi_{2496}(421, \cdot)\) None 0 8
2496.1.ed \(\chi_{2496}(395, \cdot)\) None 0 8
2496.1.eg \(\chi_{2496}(235, \cdot)\) None 0 8
2496.1.eh \(\chi_{2496}(77, \cdot)\) 2496.1.eh.a 32 8
2496.1.ei \(\chi_{2496}(457, \cdot)\) None 0 8
2496.1.ek \(\chi_{2496}(71, \cdot)\) None 0 8
2496.1.em \(\chi_{2496}(329, \cdot)\) None 0 8
2496.1.eo \(\chi_{2496}(185, \cdot)\) None 0 8
2496.1.er \(\chi_{2496}(55, \cdot)\) None 0 8
2496.1.et \(\chi_{2496}(199, \cdot)\) None 0 8
2496.1.ev \(\chi_{2496}(409, \cdot)\) None 0 8
2496.1.ex \(\chi_{2496}(119, \cdot)\) None 0 8
2496.1.ey \(\chi_{2496}(43, \cdot)\) None 0 16
2496.1.ez \(\chi_{2496}(29, \cdot)\) None 0 16
2496.1.fc \(\chi_{2496}(11, \cdot)\) None 0 16
2496.1.fd \(\chi_{2496}(37, \cdot)\) None 0 16
2496.1.fg \(\chi_{2496}(323, \cdot)\) None 0 16
2496.1.fh \(\chi_{2496}(349, \cdot)\) None 0 16
2496.1.fk \(\chi_{2496}(101, \cdot)\) None 0 16
2496.1.fl \(\chi_{2496}(139, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2496))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2496)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1248))\)\(^{\oplus 2}\)