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Properties

Label 234.2
Level 234
Weight 2
Dimension 395
Nonzero newspaces 15
Newform subspaces 37
Sturm bound 6048
Trace bound 11

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Defining parameters

Level: \( N \) = \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 37 \)
Sturm bound: \(6048\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(234))\).

Total New Old
Modular forms 1704 395 1309
Cusp forms 1321 395 926
Eisenstein series 383 0 383

Trace form

\( 395 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 8 q^{7} - q^{8} - 6 q^{9} + O(q^{10}) \) \( 395 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 8 q^{7} - q^{8} - 6 q^{9} + 15 q^{10} + 6 q^{11} + 26 q^{13} + 16 q^{14} + 6 q^{16} + 27 q^{17} + 12 q^{18} + 32 q^{19} + 3 q^{20} - 12 q^{21} - 6 q^{22} + 6 q^{24} + 5 q^{25} - 4 q^{26} - 20 q^{28} - 45 q^{29} - 48 q^{30} - 80 q^{31} + 2 q^{32} - 54 q^{33} - 78 q^{34} - 168 q^{35} - 54 q^{36} - 65 q^{37} - 110 q^{38} - 96 q^{39} - 123 q^{41} - 72 q^{42} - 70 q^{43} - 60 q^{44} - 120 q^{45} - 48 q^{46} - 108 q^{47} - 6 q^{48} - 86 q^{49} - 79 q^{50} - 66 q^{51} - 7 q^{52} - 12 q^{53} - 18 q^{54} + 60 q^{55} + 16 q^{56} - 6 q^{57} + 39 q^{58} + 54 q^{59} + 55 q^{61} + 52 q^{62} - 24 q^{63} - q^{64} - 57 q^{65} - 10 q^{67} - 3 q^{68} - 72 q^{69} + 36 q^{70} - 72 q^{71} - 6 q^{72} - 148 q^{73} + 31 q^{74} - 90 q^{75} + 26 q^{76} - 84 q^{77} + 6 q^{78} - 8 q^{79} + 3 q^{80} - 78 q^{81} + 15 q^{82} - 120 q^{83} + 12 q^{84} - 69 q^{85} + 22 q^{86} - 132 q^{87} - 6 q^{88} - 72 q^{89} - 28 q^{91} + 12 q^{92} - 72 q^{93} + 48 q^{94} - 24 q^{95} + 70 q^{97} + 108 q^{98} + 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)

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
234.2.a \(\chi_{234}(1, \cdot)\) 234.2.a.a 1 1
234.2.a.b 1
234.2.a.c 1
234.2.a.d 1
234.2.a.e 1
234.2.b \(\chi_{234}(181, \cdot)\) 234.2.b.a 2 1
234.2.b.b 2
234.2.e \(\chi_{234}(79, \cdot)\) 234.2.e.a 2 2
234.2.e.b 4
234.2.e.c 4
234.2.e.d 6
234.2.e.e 8
234.2.f \(\chi_{234}(133, \cdot)\) 234.2.f.a 2 2
234.2.f.b 2
234.2.f.c 12
234.2.f.d 12
234.2.g \(\chi_{234}(61, \cdot)\) 234.2.g.a 2 2
234.2.g.b 2
234.2.g.c 12
234.2.g.d 12
234.2.h \(\chi_{234}(55, \cdot)\) 234.2.h.a 2 2
234.2.h.b 2
234.2.h.c 2
234.2.h.d 4
234.2.h.e 4
234.2.j \(\chi_{234}(125, \cdot)\) 234.2.j.a 4 2
234.2.l \(\chi_{234}(127, \cdot)\) 234.2.l.a 4 2
234.2.l.b 4
234.2.l.c 4
234.2.p \(\chi_{234}(43, \cdot)\) 234.2.p.a 28 2
234.2.s \(\chi_{234}(121, \cdot)\) 234.2.s.a 28 2
234.2.t \(\chi_{234}(25, \cdot)\) 234.2.t.a 28 2
234.2.x \(\chi_{234}(71, \cdot)\) 234.2.x.a 8 4
234.2.x.b 16
234.2.y \(\chi_{234}(11, \cdot)\) 234.2.y.a 56 4
234.2.z \(\chi_{234}(41, \cdot)\) 234.2.z.a 56 4
234.2.bd \(\chi_{234}(5, \cdot)\) 234.2.bd.a 56 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(234))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(234)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 1}\)