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Properties

Label 371.1
Level 371
Weight 1
Dimension 37
Nonzero newspaces 5
Newform subspaces 7
Sturm bound 11232
Trace bound 2

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Defining parameters

Level: \( N \) = \( 371 = 7 \cdot 53 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 7 \)
Sturm bound: \(11232\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(371))\).

Total New Old
Modular forms 349 291 58
Cusp forms 37 37 0
Eisenstein series 312 254 58

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 29 0 8 0

Trace form

\( 37 q - 4 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 37 q - 4 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{8} + 2 q^{9} + 4 q^{10} - 3 q^{11} + 2 q^{12} - 8 q^{13} + 2 q^{14} - 12 q^{15} - 4 q^{16} + 3 q^{17} - 2 q^{19} - 2 q^{21} - 8 q^{22} - 2 q^{23} + 2 q^{25} + 2 q^{26} - 10 q^{28} - 8 q^{29} + 4 q^{30} - 8 q^{32} + 2 q^{33} + 4 q^{34} - 11 q^{36} - 3 q^{37} + 2 q^{39} - 4 q^{42} + 19 q^{44} - 4 q^{46} + 3 q^{47} + 4 q^{48} + 4 q^{49} + 2 q^{50} - 2 q^{51} + 3 q^{52} - 6 q^{53} - 8 q^{55} - 4 q^{56} - 4 q^{57} - 6 q^{58} - 3 q^{59} - 4 q^{60} - 2 q^{61} + 3 q^{63} + 23 q^{64} - 4 q^{65} + 4 q^{66} - 7 q^{68} - 6 q^{71} - 4 q^{72} - 2 q^{73} - 6 q^{74} - 2 q^{75} + 4 q^{76} - 3 q^{77} - 2 q^{79} - 4 q^{81} + 4 q^{83} + 4 q^{84} - 2 q^{86} - 2 q^{87} + 18 q^{88} + 3 q^{89} + 3 q^{91} - 6 q^{92} + 4 q^{93} + 2 q^{94} + 8 q^{95} + 26 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(371))\)

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
371.1.c \(\chi_{371}(370, \cdot)\) 371.1.c.a 1 1
371.1.c.b 2
371.1.d \(\chi_{371}(160, \cdot)\) None 0 1
371.1.f \(\chi_{371}(288, \cdot)\) None 0 2
371.1.h \(\chi_{371}(54, \cdot)\) None 0 2
371.1.i \(\chi_{371}(52, \cdot)\) 371.1.i.a 2 2
371.1.k \(\chi_{371}(23, \cdot)\) 371.1.k.a 4 4
371.1.k.b 4
371.1.n \(\chi_{371}(13, \cdot)\) 371.1.n.a 12 12
371.1.o \(\chi_{371}(6, \cdot)\) 371.1.o.a 12 12
371.1.s \(\chi_{371}(8, \cdot)\) None 0 24
371.1.u \(\chi_{371}(17, \cdot)\) None 0 24
371.1.v \(\chi_{371}(10, \cdot)\) None 0 24
371.1.x \(\chi_{371}(2, \cdot)\) None 0 48