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Properties

Label 1815.1
Level 1815
Weight 1
Dimension 66
Nonzero newspaces 3
Newform subspaces 18
Sturm bound 232320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 18 \)
Sturm bound: \(232320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1815))\).

Total New Old
Modular forms 2676 908 1768
Cusp forms 116 66 50
Eisenstein series 2560 842 1718

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 66 0 0 0

Trace form

\( 66 q + 2 q^{3} + O(q^{10}) \) \( 66 q + 2 q^{3} + 8 q^{12} + 2 q^{15} + 4 q^{16} + 4 q^{25} + 2 q^{27} - 40 q^{34} - 4 q^{37} - 2 q^{48} - 2 q^{60} - 16 q^{67} - 2 q^{75} - 4 q^{81} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1815))\)

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
1815.1.b \(\chi_{1815}(241, \cdot)\) None 0 1
1815.1.e \(\chi_{1815}(1211, \cdot)\) None 0 1
1815.1.g \(\chi_{1815}(1574, \cdot)\) 1815.1.g.a 1 1
1815.1.g.b 1
1815.1.g.c 1
1815.1.g.d 1
1815.1.g.e 1
1815.1.g.f 1
1815.1.g.g 2
1815.1.g.h 2
1815.1.h \(\chi_{1815}(604, \cdot)\) None 0 1
1815.1.i \(\chi_{1815}(727, \cdot)\) None 0 2
1815.1.l \(\chi_{1815}(362, \cdot)\) None 0 2
1815.1.n \(\chi_{1815}(94, \cdot)\) None 0 4
1815.1.o \(\chi_{1815}(269, \cdot)\) 1815.1.o.a 4 4
1815.1.o.b 4
1815.1.o.c 4
1815.1.o.d 4
1815.1.o.e 4
1815.1.o.f 4
1815.1.o.g 8
1815.1.o.h 8
1815.1.q \(\chi_{1815}(251, \cdot)\) None 0 4
1815.1.t \(\chi_{1815}(481, \cdot)\) None 0 4
1815.1.v \(\chi_{1815}(233, \cdot)\) 1815.1.v.a 8 8
1815.1.v.b 8
1815.1.y \(\chi_{1815}(148, \cdot)\) None 0 8
1815.1.z \(\chi_{1815}(109, \cdot)\) None 0 10
1815.1.ba \(\chi_{1815}(89, \cdot)\) None 0 10
1815.1.bc \(\chi_{1815}(56, \cdot)\) None 0 10
1815.1.bf \(\chi_{1815}(76, \cdot)\) None 0 10
1815.1.bg \(\chi_{1815}(32, \cdot)\) None 0 20
1815.1.bj \(\chi_{1815}(67, \cdot)\) None 0 20
1815.1.bl \(\chi_{1815}(46, \cdot)\) None 0 40
1815.1.bo \(\chi_{1815}(26, \cdot)\) None 0 40
1815.1.bq \(\chi_{1815}(14, \cdot)\) None 0 40
1815.1.br \(\chi_{1815}(19, \cdot)\) None 0 40
1815.1.bs \(\chi_{1815}(37, \cdot)\) None 0 80
1815.1.bv \(\chi_{1815}(2, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1815))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1815)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 2}\)