Properties

Label 148.1
Level 148
Weight 1
Dimension 10
Nonzero newspaces 3
Newforms 3
Sturm bound 1368
Trace bound 2

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Defining parameters

Level: \( N \) = \( 148 = 2^{2} \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 3 \)
Sturm bound: \(1368\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(148))\).

Total New Old
Modular forms 100 44 56
Cusp forms 10 10 0
Eisenstein series 90 34 56

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 2 0

Trace form

\(10q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 3q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut +\mathstrut 8q^{36} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut +\mathstrut 7q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut +\mathstrut 6q^{50} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 2q^{71} \) \(\mathstrut -\mathstrut q^{72} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut 3q^{81} \) \(\mathstrut -\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 2q^{83} \) \(\mathstrut +\mathstrut 5q^{85} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut +\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)

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
148.1.b \(\chi_{148}(147, \cdot)\) None 0 1
148.1.c \(\chi_{148}(75, \cdot)\) None 0 1
148.1.f \(\chi_{148}(105, \cdot)\) 148.1.f.a 2 2
148.1.i \(\chi_{148}(47, \cdot)\) 148.1.i.a 2 2
148.1.j \(\chi_{148}(11, \cdot)\) None 0 2
148.1.m \(\chi_{148}(29, \cdot)\) None 0 4
148.1.o \(\chi_{148}(3, \cdot)\) None 0 6
148.1.p \(\chi_{148}(7, \cdot)\) 148.1.p.a 6 6
148.1.r \(\chi_{148}(5, \cdot)\) None 0 12