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Properties

Label 975.1
Level 975
Weight 1
Dimension 95
Nonzero newspaces 13
Newform subspaces 19
Sturm bound 67200
Trace bound 9

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Defining parameters

Level: \( N \) = \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 13 \)
Newform subspaces: \( 19 \)
Sturm bound: \(67200\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(975))\).

Total New Old
Modular forms 1466 545 921
Cusp forms 122 95 27
Eisenstein series 1344 450 894

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 79 0 0 16

Trace form

\( 95 q + q^{3} - q^{4} - 6 q^{6} - 8 q^{7} + q^{9} + O(q^{10}) \) \( 95 q + q^{3} - q^{4} - 6 q^{6} - 8 q^{7} + q^{9} - 2 q^{10} - 9 q^{12} + 5 q^{13} + 2 q^{15} - 17 q^{16} + 2 q^{19} - 8 q^{21} - 8 q^{24} + 4 q^{25} + q^{27} - 6 q^{28} - 8 q^{30} - 8 q^{31} + 6 q^{33} - 8 q^{34} - 11 q^{36} - 2 q^{37} - 13 q^{39} - 4 q^{40} - 6 q^{42} - 6 q^{43} + 6 q^{46} - 7 q^{48} + 3 q^{49} - 16 q^{51} - 13 q^{52} + 6 q^{54} - 6 q^{55} - 8 q^{60} - 4 q^{61} - 2 q^{63} + 29 q^{64} - 8 q^{66} + 4 q^{67} + 2 q^{69} - 12 q^{70} + 4 q^{73} - 4 q^{76} + 6 q^{78} + 2 q^{79} - 7 q^{81} + 36 q^{82} + 2 q^{85} + 28 q^{88} - 8 q^{90} - 10 q^{91} + 14 q^{94} - 4 q^{96} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(975))\)

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
975.1.d \(\chi_{975}(326, \cdot)\) None 0 1
975.1.e \(\chi_{975}(974, \cdot)\) 975.1.e.a 2 1
975.1.f \(\chi_{975}(599, \cdot)\) None 0 1
975.1.g \(\chi_{975}(701, \cdot)\) 975.1.g.a 1 1
975.1.g.b 2
975.1.g.c 2
975.1.j \(\chi_{975}(593, \cdot)\) 975.1.j.a 4 2
975.1.l \(\chi_{975}(493, \cdot)\) None 0 2
975.1.p \(\chi_{975}(151, \cdot)\) None 0 2
975.1.q \(\chi_{975}(424, \cdot)\) None 0 2
975.1.r \(\chi_{975}(118, \cdot)\) None 0 2
975.1.u \(\chi_{975}(632, \cdot)\) 975.1.u.a 4 2
975.1.x \(\chi_{975}(101, \cdot)\) 975.1.x.a 2 2
975.1.x.b 2
975.1.y \(\chi_{975}(74, \cdot)\) 975.1.y.a 4 2
975.1.z \(\chi_{975}(374, \cdot)\) 975.1.z.a 4 2
975.1.ba \(\chi_{975}(776, \cdot)\) 975.1.ba.a 2 2
975.1.ba.b 2
975.1.bd \(\chi_{975}(116, \cdot)\) 975.1.bd.a 4 4
975.1.bd.b 4
975.1.bd.c 8
975.1.be \(\chi_{975}(14, \cdot)\) None 0 4
975.1.bi \(\chi_{975}(194, \cdot)\) 975.1.bi.a 16 4
975.1.bj \(\chi_{975}(131, \cdot)\) None 0 4
975.1.bk \(\chi_{975}(332, \cdot)\) 975.1.bk.a 8 4
975.1.bm \(\chi_{975}(568, \cdot)\) None 0 4
975.1.bq \(\chi_{975}(124, \cdot)\) None 0 4
975.1.br \(\chi_{975}(76, \cdot)\) None 0 4
975.1.bs \(\chi_{975}(43, \cdot)\) None 0 4
975.1.bv \(\chi_{975}(32, \cdot)\) 975.1.bv.a 8 4
975.1.by \(\chi_{975}(47, \cdot)\) None 0 8
975.1.ca \(\chi_{975}(313, \cdot)\) None 0 8
975.1.cb \(\chi_{975}(34, \cdot)\) None 0 8
975.1.cc \(\chi_{975}(31, \cdot)\) None 0 8
975.1.cg \(\chi_{975}(103, \cdot)\) None 0 8
975.1.ch \(\chi_{975}(8, \cdot)\) None 0 8
975.1.cj \(\chi_{975}(146, \cdot)\) 975.1.cj.a 16 8
975.1.ck \(\chi_{975}(134, \cdot)\) None 0 8
975.1.co \(\chi_{975}(29, \cdot)\) None 0 8
975.1.cp \(\chi_{975}(56, \cdot)\) None 0 8
975.1.cr \(\chi_{975}(2, \cdot)\) None 0 16
975.1.ct \(\chi_{975}(88, \cdot)\) None 0 16
975.1.cu \(\chi_{975}(46, \cdot)\) None 0 16
975.1.cv \(\chi_{975}(19, \cdot)\) None 0 16
975.1.cz \(\chi_{975}(22, \cdot)\) None 0 16
975.1.da \(\chi_{975}(137, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(975))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(975)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 2}\)