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Properties

Label 423.2
Level 423
Weight 2
Dimension 5037
Nonzero newspaces 8
Newform subspaces 28
Sturm bound 26496
Trace bound 2

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Defining parameters

Level: \( N \) = \( 423 = 3^{2} \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 28 \)
Sturm bound: \(26496\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(423))\).

Total New Old
Modular forms 6992 5441 1551
Cusp forms 6257 5037 1220
Eisenstein series 735 404 331

Trace form

\( 5037 q - 69 q^{2} - 92 q^{3} - 69 q^{4} - 69 q^{5} - 92 q^{6} - 69 q^{7} - 69 q^{8} - 92 q^{9} + O(q^{10}) \) \( 5037 q - 69 q^{2} - 92 q^{3} - 69 q^{4} - 69 q^{5} - 92 q^{6} - 69 q^{7} - 69 q^{8} - 92 q^{9} - 207 q^{10} - 69 q^{11} - 92 q^{12} - 69 q^{13} - 69 q^{14} - 92 q^{15} - 69 q^{16} - 69 q^{17} - 92 q^{18} - 207 q^{19} - 69 q^{20} - 92 q^{21} - 69 q^{22} - 69 q^{23} - 92 q^{24} - 69 q^{25} - 69 q^{26} - 92 q^{27} - 207 q^{28} - 69 q^{29} - 92 q^{30} - 69 q^{31} - 69 q^{32} - 92 q^{33} - 69 q^{34} - 92 q^{35} - 92 q^{36} - 230 q^{37} - 115 q^{38} - 92 q^{39} - 207 q^{40} - 138 q^{41} - 92 q^{42} - 92 q^{43} - 161 q^{44} - 92 q^{45} - 322 q^{46} - 115 q^{47} - 184 q^{48} - 115 q^{49} - 161 q^{50} - 92 q^{51} - 161 q^{52} - 92 q^{53} - 92 q^{54} - 276 q^{55} - 207 q^{56} - 92 q^{57} - 115 q^{58} - 92 q^{59} - 92 q^{60} - 92 q^{61} - 69 q^{62} - 92 q^{63} - 207 q^{64} - 69 q^{65} - 92 q^{66} - 69 q^{67} - 69 q^{68} - 92 q^{69} - 69 q^{70} - 69 q^{71} - 92 q^{72} - 207 q^{73} - 69 q^{74} - 92 q^{75} - 115 q^{76} - 115 q^{77} - 92 q^{78} - 161 q^{79} - 230 q^{80} - 92 q^{81} - 414 q^{82} - 115 q^{83} - 92 q^{84} - 253 q^{85} - 253 q^{86} - 92 q^{87} - 345 q^{88} - 161 q^{89} - 92 q^{90} - 437 q^{91} - 138 q^{92} - 92 q^{93} - 345 q^{94} - 322 q^{95} - 92 q^{96} - 161 q^{97} - 276 q^{98} - 92 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(423))\)

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
423.2.a \(\chi_{423}(1, \cdot)\) 423.2.a.a 1 1
423.2.a.b 1
423.2.a.c 1
423.2.a.d 1
423.2.a.e 1
423.2.a.f 1
423.2.a.g 1
423.2.a.h 2
423.2.a.i 3
423.2.a.j 3
423.2.a.k 4
423.2.c \(\chi_{423}(422, \cdot)\) 423.2.c.a 4 1
423.2.c.b 4
423.2.c.c 8
423.2.e \(\chi_{423}(142, \cdot)\) 423.2.e.a 2 2
423.2.e.b 2
423.2.e.c 2
423.2.e.d 34
423.2.e.e 52
423.2.g \(\chi_{423}(140, \cdot)\) 423.2.g.a 20 2
423.2.g.b 72
423.2.i \(\chi_{423}(28, \cdot)\) 423.2.i.a 66 22
423.2.i.b 88
423.2.i.c 88
423.2.i.d 176
423.2.k \(\chi_{423}(26, \cdot)\) 423.2.k.a 352 22
423.2.m \(\chi_{423}(4, \cdot)\) 423.2.m.a 2024 44
423.2.o \(\chi_{423}(5, \cdot)\) 423.2.o.a 2024 44

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(423))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(423)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 2}\)