Properties

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

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Defining parameters

Level: \( N \) = \( 633 = 3 \cdot 211 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 4 \)
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

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

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 the 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

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