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Properties

Label 2120.1
Level 2120
Weight 1
Dimension 74
Nonzero newspaces 5
Newform subspaces 11
Sturm bound 269568
Trace bound 6

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Defining parameters

Level: \( N \) = \( 2120 = 2^{3} \cdot 5 \cdot 53 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 11 \)
Sturm bound: \(269568\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2120))\).

Total New Old
Modular forms 2786 686 2100
Cusp forms 290 74 216
Eisenstein series 2496 612 1884

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 74 0 0 0

Trace form

\( 74 q + 6 q^{4} - 12 q^{6} - 4 q^{7} + 2 q^{9} + O(q^{10}) \) \( 74 q + 6 q^{4} - 12 q^{6} - 4 q^{7} + 2 q^{9} + 8 q^{10} - 4 q^{11} - 4 q^{14} + 6 q^{16} - 4 q^{17} - 4 q^{19} - 4 q^{24} + 12 q^{25} + 4 q^{28} - 4 q^{31} - 4 q^{35} + 26 q^{36} + 4 q^{38} - 4 q^{40} + 8 q^{42} - 12 q^{44} - 8 q^{46} - 4 q^{47} - 6 q^{49} - 8 q^{54} - 4 q^{56} + 8 q^{57} - 4 q^{59} - 8 q^{60} - 12 q^{63} + 6 q^{64} - 8 q^{66} + 4 q^{68} - 8 q^{70} + 4 q^{71} - 8 q^{74} - 4 q^{76} - 4 q^{79} - 18 q^{81} - 4 q^{86} - 12 q^{89} - 4 q^{90} - 16 q^{91} - 4 q^{94} - 4 q^{95} + 4 q^{96} + 4 q^{97} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2120))\)

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
2120.1.c \(\chi_{2120}(1591, \cdot)\) None 0 1
2120.1.e \(\chi_{2120}(211, \cdot)\) None 0 1
2120.1.f \(\chi_{2120}(2119, \cdot)\) None 0 1
2120.1.h \(\chi_{2120}(1379, \cdot)\) None 0 1
2120.1.k \(\chi_{2120}(1271, \cdot)\) None 0 1
2120.1.m \(\chi_{2120}(531, \cdot)\) None 0 1
2120.1.n \(\chi_{2120}(319, \cdot)\) None 0 1
2120.1.p \(\chi_{2120}(1059, \cdot)\) 2120.1.p.a 2 1
2120.1.p.b 3
2120.1.p.c 3
2120.1.p.d 3
2120.1.p.e 3
2120.1.p.f 4
2120.1.q \(\chi_{2120}(83, \cdot)\) None 0 2
2120.1.t \(\chi_{2120}(23, \cdot)\) None 0 2
2120.1.u \(\chi_{2120}(401, \cdot)\) None 0 2
2120.1.w \(\chi_{2120}(341, \cdot)\) None 0 2
2120.1.z \(\chi_{2120}(317, \cdot)\) 2120.1.z.a 4 2
2120.1.ba \(\chi_{2120}(213, \cdot)\) None 0 2
2120.1.bd \(\chi_{2120}(1273, \cdot)\) None 0 2
2120.1.be \(\chi_{2120}(953, \cdot)\) None 0 2
2120.1.bh \(\chi_{2120}(129, \cdot)\) None 0 2
2120.1.bj \(\chi_{2120}(189, \cdot)\) 2120.1.bj.a 4 2
2120.1.bl \(\chi_{2120}(507, \cdot)\) None 0 2
2120.1.bm \(\chi_{2120}(447, \cdot)\) None 0 2
2120.1.bp \(\chi_{2120}(59, \cdot)\) 2120.1.bp.a 24 12
2120.1.br \(\chi_{2120}(119, \cdot)\) None 0 12
2120.1.bs \(\chi_{2120}(331, \cdot)\) None 0 12
2120.1.bu \(\chi_{2120}(271, \cdot)\) None 0 12
2120.1.bx \(\chi_{2120}(99, \cdot)\) 2120.1.bx.a 12 12
2120.1.bx.b 12
2120.1.bz \(\chi_{2120}(199, \cdot)\) None 0 12
2120.1.ca \(\chi_{2120}(11, \cdot)\) None 0 12
2120.1.cc \(\chi_{2120}(311, \cdot)\) None 0 12
2120.1.ce \(\chi_{2120}(87, \cdot)\) None 0 24
2120.1.ch \(\chi_{2120}(147, \cdot)\) None 0 24
2120.1.ci \(\chi_{2120}(109, \cdot)\) None 0 24
2120.1.ck \(\chi_{2120}(209, \cdot)\) None 0 24
2120.1.cn \(\chi_{2120}(17, \cdot)\) None 0 24
2120.1.co \(\chi_{2120}(97, \cdot)\) None 0 24
2120.1.cr \(\chi_{2120}(13, \cdot)\) None 0 24
2120.1.cs \(\chi_{2120}(37, \cdot)\) None 0 24
2120.1.cv \(\chi_{2120}(21, \cdot)\) None 0 24
2120.1.cx \(\chi_{2120}(41, \cdot)\) None 0 24
2120.1.cz \(\chi_{2120}(103, \cdot)\) None 0 24
2120.1.da \(\chi_{2120}(3, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2120))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2120)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(212))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(265))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(424))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(530))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1060))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2120))\)\(^{\oplus 1}\)