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Properties

Label 148.2
Level 148
Weight 2
Dimension 363
Nonzero newspaces 9
Newform subspaces 16
Sturm bound 2736
Trace bound 1

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Defining parameters

Level: \( N \) = \( 148 = 2^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 16 \)
Sturm bound: \(2736\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(148))\).

Total New Old
Modular forms 774 435 339
Cusp forms 595 363 232
Eisenstein series 179 72 107

Trace form

\( 363 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} + O(q^{10}) \) \( 363 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 18 q^{26} - 24 q^{27} - 18 q^{28} - 54 q^{29} - 18 q^{30} - 54 q^{31} - 18 q^{32} - 72 q^{33} - 18 q^{34} - 54 q^{35} - 78 q^{37} - 36 q^{38} - 42 q^{39} - 18 q^{40} - 90 q^{41} - 18 q^{42} - 36 q^{43} - 18 q^{44} - 90 q^{45} - 18 q^{46} - 18 q^{47} - 18 q^{48} - 60 q^{49} - 18 q^{50} - 18 q^{52} - 36 q^{53} - 18 q^{54} - 18 q^{56} - 36 q^{57} + 36 q^{59} + 108 q^{60} + 9 q^{61} + 72 q^{62} + 108 q^{63} + 108 q^{64} + 45 q^{65} + 234 q^{66} + 36 q^{67} + 90 q^{68} + 108 q^{69} + 180 q^{70} + 72 q^{71} + 234 q^{72} + 72 q^{73} + 126 q^{74} + 180 q^{75} + 126 q^{76} + 36 q^{77} + 234 q^{78} + 72 q^{79} + 180 q^{80} + 108 q^{81} + 90 q^{82} + 36 q^{83} + 234 q^{84} + 45 q^{85} + 108 q^{86} + 108 q^{87} + 72 q^{88} + 9 q^{89} + 108 q^{90} + 30 q^{91} - 90 q^{93} - 18 q^{94} - 72 q^{95} - 18 q^{96} - 108 q^{97} - 18 q^{98} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)

We only show spaces with even 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
148.2.a \(\chi_{148}(1, \cdot)\) 148.2.a.a 1 1
148.2.a.b 2
148.2.d \(\chi_{148}(73, \cdot)\) 148.2.d.a 2 1
148.2.e \(\chi_{148}(121, \cdot)\) 148.2.e.a 6 2
148.2.g \(\chi_{148}(31, \cdot)\) 148.2.g.a 2 2
148.2.g.b 4
148.2.g.c 28
148.2.h \(\chi_{148}(85, \cdot)\) 148.2.h.a 2 2
148.2.h.b 2
148.2.k \(\chi_{148}(9, \cdot)\) 148.2.k.a 24 6
148.2.l \(\chi_{148}(23, \cdot)\) 148.2.l.a 4 4
148.2.l.b 64
148.2.n \(\chi_{148}(21, \cdot)\) 148.2.n.a 6 6
148.2.n.b 12
148.2.q \(\chi_{148}(15, \cdot)\) 148.2.q.a 12 12
148.2.q.b 192

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(148))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(148)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 2}\)