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Properties

Label 633.1
Level 633
Weight 1
Dimension 42
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 29680
Trace bound 1

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Defining parameters

Level: \( N \) = \( 633 = 3 \cdot 211 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(29680\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(633))\).

Total New Old
Modular forms 464 250 214
Cusp forms 44 42 2
Eisenstein series 420 208 212

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 34 0 0 8

Trace form

\( 42 q + q^{3} - 5 q^{4} - 4 q^{7} - 3 q^{9} + O(q^{10}) \) \( 42 q + q^{3} - 5 q^{4} - 4 q^{7} - 3 q^{9} + 4 q^{10} + 3 q^{12} - q^{16} - 4 q^{19} - 2 q^{22} - q^{25} + q^{27} + 4 q^{28} + 6 q^{30} - 6 q^{31} - 8 q^{34} - 5 q^{36} - 2 q^{37} - 4 q^{39} - 8 q^{40} - 10 q^{43} + 4 q^{46} - q^{48} - 3 q^{49} - 8 q^{52} + 4 q^{55} + 12 q^{58} - 8 q^{61} + 6 q^{63} - 7 q^{64} + 2 q^{66} - 2 q^{67} + 4 q^{70} - 10 q^{73} - q^{75} + 4 q^{76} - 2 q^{79} - 3 q^{81} + 2 q^{82} - 8 q^{84} - 4 q^{85} + 4 q^{88} - 6 q^{90} - 2 q^{91} + 2 q^{93} - 12 q^{94} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(633))\)

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
633.1.b \(\chi_{633}(212, \cdot)\) None 0 1
633.1.c \(\chi_{633}(421, \cdot)\) None 0 1
633.1.h \(\chi_{633}(14, \cdot)\) None 0 2
633.1.i \(\chi_{633}(226, \cdot)\) None 0 2
633.1.l \(\chi_{633}(367, \cdot)\) None 0 4
633.1.m \(\chi_{633}(71, \cdot)\) 633.1.m.a 4 4
633.1.m.b 8
633.1.o \(\chi_{633}(40, \cdot)\) None 0 6
633.1.p \(\chi_{633}(269, \cdot)\) 633.1.p.a 6 6
633.1.s \(\chi_{633}(10, \cdot)\) None 0 8
633.1.t \(\chi_{633}(83, \cdot)\) None 0 8
633.1.w \(\chi_{633}(31, \cdot)\) None 0 12
633.1.x \(\chi_{633}(101, \cdot)\) None 0 12
633.1.z \(\chi_{633}(5, \cdot)\) 633.1.z.a 24 24
633.1.ba \(\chi_{633}(28, \cdot)\) None 0 24
633.1.be \(\chi_{633}(20, \cdot)\) None 0 48
633.1.bf \(\chi_{633}(7, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(633))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(633)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(211))\)\(^{\oplus 2}\)