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Properties

Label 1300.1
Level 1300
Weight 1
Dimension 128
Nonzero newspaces 18
Newform subspaces 28
Sturm bound 100800
Trace bound 29

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Defining parameters

Level: \( N \) = \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 28 \)
Sturm bound: \(100800\)
Trace bound: \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1300))\).

Total New Old
Modular forms 1882 578 1304
Cusp forms 202 128 74
Eisenstein series 1680 450 1230

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 120 0 8 0

Trace form

\( 128 q + 3 q^{2} + 3 q^{4} + 2 q^{5} + 6 q^{8} + 3 q^{9} + O(q^{10}) \) \( 128 q + 3 q^{2} + 3 q^{4} + 2 q^{5} + 6 q^{8} + 3 q^{9} + 2 q^{10} + 8 q^{11} + 3 q^{13} + 7 q^{16} + 9 q^{17} - 4 q^{18} - 8 q^{20} + 2 q^{25} - q^{26} + 9 q^{29} - 7 q^{32} - 4 q^{34} + 7 q^{36} - q^{37} + 2 q^{40} + 9 q^{41} + 2 q^{45} - 7 q^{49} - 10 q^{50} - 18 q^{52} - 4 q^{53} - 8 q^{56} - 15 q^{58} - 15 q^{61} - 18 q^{64} - 3 q^{65} - 15 q^{68} - 8 q^{71} + 3 q^{72} + 6 q^{73} - 15 q^{74} - 10 q^{80} - q^{81} - 15 q^{82} - 6 q^{85} - 4 q^{89} + 2 q^{90} + 6 q^{97} + 3 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1300))\)

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
1300.1.b \(\chi_{1300}(651, \cdot)\) None 0 1
1300.1.e \(\chi_{1300}(51, \cdot)\) 1300.1.e.a 1 1
1300.1.e.b 1
1300.1.e.c 1
1300.1.e.d 1
1300.1.e.e 2
1300.1.g \(\chi_{1300}(1299, \cdot)\) 1300.1.g.a 2 1
1300.1.g.b 2
1300.1.h \(\chi_{1300}(599, \cdot)\) None 0 1
1300.1.k \(\chi_{1300}(749, \cdot)\) 1300.1.k.a 2 2
1300.1.k.b 2
1300.1.l \(\chi_{1300}(307, \cdot)\) 1300.1.l.a 2 2
1300.1.n \(\chi_{1300}(493, \cdot)\) None 0 2
1300.1.q \(\chi_{1300}(157, \cdot)\) None 0 2
1300.1.s \(\chi_{1300}(707, \cdot)\) 1300.1.s.a 2 2
1300.1.t \(\chi_{1300}(801, \cdot)\) 1300.1.t.a 2 2
1300.1.t.b 2
1300.1.w \(\chi_{1300}(399, \cdot)\) 1300.1.w.a 4 2
1300.1.x \(\chi_{1300}(199, \cdot)\) None 0 2
1300.1.z \(\chi_{1300}(251, \cdot)\) 1300.1.z.a 4 2
1300.1.bc \(\chi_{1300}(451, \cdot)\) 1300.1.bc.a 2 2
1300.1.bd \(\chi_{1300}(259, \cdot)\) 1300.1.bd.a 4 4
1300.1.bd.b 4
1300.1.bf \(\chi_{1300}(79, \cdot)\) None 0 4
1300.1.bh \(\chi_{1300}(131, \cdot)\) None 0 4
1300.1.bi \(\chi_{1300}(311, \cdot)\) None 0 4
1300.1.bl \(\chi_{1300}(201, \cdot)\) None 0 4
1300.1.bm \(\chi_{1300}(843, \cdot)\) 1300.1.bm.a 4 4
1300.1.bp \(\chi_{1300}(393, \cdot)\) None 0 4
1300.1.bq \(\chi_{1300}(257, \cdot)\) None 0 4
1300.1.bt \(\chi_{1300}(7, \cdot)\) 1300.1.bt.a 4 4
1300.1.bu \(\chi_{1300}(149, \cdot)\) None 0 4
1300.1.by \(\chi_{1300}(21, \cdot)\) None 0 8
1300.1.ca \(\chi_{1300}(47, \cdot)\) 1300.1.ca.a 8 8
1300.1.cb \(\chi_{1300}(53, \cdot)\) None 0 8
1300.1.ce \(\chi_{1300}(77, \cdot)\) None 0 8
1300.1.cf \(\chi_{1300}(187, \cdot)\) 1300.1.cf.a 8 8
1300.1.ch \(\chi_{1300}(109, \cdot)\) None 0 8
1300.1.ck \(\chi_{1300}(231, \cdot)\) None 0 8
1300.1.cl \(\chi_{1300}(191, \cdot)\) 1300.1.cl.a 8 8
1300.1.cl.b 8
1300.1.cn \(\chi_{1300}(139, \cdot)\) None 0 8
1300.1.cp \(\chi_{1300}(179, \cdot)\) 1300.1.cp.a 8 8
1300.1.cp.b 8
1300.1.cr \(\chi_{1300}(89, \cdot)\) None 0 16
1300.1.ct \(\chi_{1300}(63, \cdot)\) 1300.1.ct.a 16 16
1300.1.cv \(\chi_{1300}(17, \cdot)\) None 0 16
1300.1.cw \(\chi_{1300}(113, \cdot)\) None 0 16
1300.1.cy \(\chi_{1300}(123, \cdot)\) 1300.1.cy.a 16 16
1300.1.da \(\chi_{1300}(41, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1300))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1300)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 3}\)