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Properties

Label 1305.1
Level 1305
Weight 1
Dimension 12
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 120960
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(120960\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1305))\).

Total New Old
Modular forms 1840 740 1100
Cusp forms 48 12 36
Eisenstein series 1792 728 1064

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 8 0

Trace form

\( 12 q - 2 q^{7} + O(q^{10}) \) \( 12 q - 2 q^{7} + 2 q^{11} + 2 q^{13} - 12 q^{16} - 2 q^{19} + 2 q^{23} - 4 q^{25} + 2 q^{28} + 2 q^{31} + 8 q^{34} - 2 q^{35} - 2 q^{41} - 2 q^{44} + 2 q^{49} + 2 q^{52} + 2 q^{53} - 2 q^{55} + 2 q^{61} - 8 q^{64} - 2 q^{65} + 2 q^{67} + 2 q^{76} - 2 q^{79} - 2 q^{83} + 2 q^{89} - 12 q^{91} + 2 q^{92} - 8 q^{94} + 2 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1305))\)

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
1305.1.b \(\chi_{1305}(1304, \cdot)\) 1305.1.b.a 4 1
1305.1.b.b 4
1305.1.e \(\chi_{1305}(1016, \cdot)\) None 0 1
1305.1.g \(\chi_{1305}(494, \cdot)\) None 0 1
1305.1.h \(\chi_{1305}(521, \cdot)\) None 0 1
1305.1.j \(\chi_{1305}(17, \cdot)\) None 0 2
1305.1.l \(\chi_{1305}(244, \cdot)\) 1305.1.l.a 2 2
1305.1.o \(\chi_{1305}(28, \cdot)\) 1305.1.o.a 2 2
1305.1.p \(\chi_{1305}(262, \cdot)\) None 0 2
1305.1.s \(\chi_{1305}(46, \cdot)\) None 0 2
1305.1.u \(\chi_{1305}(278, \cdot)\) None 0 2
1305.1.v \(\chi_{1305}(86, \cdot)\) None 0 2
1305.1.x \(\chi_{1305}(59, \cdot)\) None 0 2
1305.1.z \(\chi_{1305}(146, \cdot)\) None 0 2
1305.1.ba \(\chi_{1305}(434, \cdot)\) None 0 2
1305.1.be \(\chi_{1305}(302, \cdot)\) None 0 4
1305.1.bf \(\chi_{1305}(331, \cdot)\) None 0 4
1305.1.bh \(\chi_{1305}(88, \cdot)\) None 0 4
1305.1.bk \(\chi_{1305}(202, \cdot)\) None 0 4
1305.1.bm \(\chi_{1305}(394, \cdot)\) None 0 4
1305.1.bn \(\chi_{1305}(128, \cdot)\) None 0 4
1305.1.bp \(\chi_{1305}(71, \cdot)\) None 0 6
1305.1.bq \(\chi_{1305}(314, \cdot)\) None 0 6
1305.1.bs \(\chi_{1305}(161, \cdot)\) None 0 6
1305.1.bv \(\chi_{1305}(179, \cdot)\) None 0 6
1305.1.bx \(\chi_{1305}(98, \cdot)\) None 0 12
1305.1.bz \(\chi_{1305}(271, \cdot)\) None 0 12
1305.1.cc \(\chi_{1305}(82, \cdot)\) None 0 12
1305.1.cd \(\chi_{1305}(208, \cdot)\) None 0 12
1305.1.cg \(\chi_{1305}(19, \cdot)\) None 0 12
1305.1.ci \(\chi_{1305}(8, \cdot)\) None 0 12
1305.1.ck \(\chi_{1305}(149, \cdot)\) None 0 12
1305.1.cl \(\chi_{1305}(281, \cdot)\) None 0 12
1305.1.cn \(\chi_{1305}(74, \cdot)\) None 0 12
1305.1.cp \(\chi_{1305}(236, \cdot)\) None 0 12
1305.1.cr \(\chi_{1305}(2, \cdot)\) None 0 24
1305.1.cs \(\chi_{1305}(79, \cdot)\) None 0 24
1305.1.cu \(\chi_{1305}(13, \cdot)\) None 0 24
1305.1.cx \(\chi_{1305}(7, \cdot)\) None 0 24
1305.1.cz \(\chi_{1305}(31, \cdot)\) None 0 24
1305.1.da \(\chi_{1305}(47, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1305))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1305)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1305))\)\(^{\oplus 1}\)