Properties

Label 234.4
Level 234
Weight 4
Dimension 1183
Nonzero newspaces 15
Newform subspaces 49
Sturm bound 12096
Trace bound 11

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Defining parameters

Level: \( N \) = \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 49 \)
Sturm bound: \(12096\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(234))\).

Total New Old
Modular forms 4728 1183 3545
Cusp forms 4344 1183 3161
Eisenstein series 384 0 384

Trace form

\( 1183 q - 8 q^{2} - 6 q^{3} + 16 q^{4} - 24 q^{5} + 36 q^{6} + 80 q^{7} + 40 q^{8} + 210 q^{9} + O(q^{10}) \) \( 1183 q - 8 q^{2} - 6 q^{3} + 16 q^{4} - 24 q^{5} + 36 q^{6} + 80 q^{7} + 40 q^{8} + 210 q^{9} - 66 q^{10} - 174 q^{11} - 48 q^{12} - 302 q^{13} - 256 q^{14} - 180 q^{15} + 64 q^{16} + 141 q^{17} - 312 q^{18} + 224 q^{19} + 36 q^{20} + 72 q^{21} + 84 q^{22} + 636 q^{23} + 48 q^{24} + 241 q^{25} + 316 q^{26} - 544 q^{28} - 3183 q^{29} - 1056 q^{30} - 1264 q^{31} - 128 q^{32} - 954 q^{33} + 612 q^{34} + 2604 q^{35} + 504 q^{36} + 2453 q^{37} + 3380 q^{38} + 4230 q^{39} + 96 q^{40} + 5283 q^{41} + 3504 q^{42} + 1694 q^{43} + 1296 q^{44} + 924 q^{45} - 1632 q^{46} - 2916 q^{47} + 288 q^{48} - 4884 q^{49} - 7202 q^{50} - 5358 q^{51} - 1508 q^{52} + 384 q^{53} - 1908 q^{54} + 2664 q^{55} - 448 q^{56} - 1974 q^{57} - 978 q^{58} - 1830 q^{59} + 1872 q^{60} - 1303 q^{61} + 1592 q^{62} - 2796 q^{63} - 1088 q^{64} - 11397 q^{65} - 576 q^{66} - 9346 q^{67} - 1476 q^{68} - 2628 q^{69} - 2040 q^{70} + 6720 q^{71} + 48 q^{72} + 9440 q^{73} + 158 q^{74} + 2058 q^{75} + 3416 q^{76} + 15912 q^{77} - 132 q^{78} + 14924 q^{79} + 1872 q^{80} + 5610 q^{81} + 5862 q^{82} + 6528 q^{83} - 1488 q^{84} + 717 q^{85} - 1300 q^{86} + 5160 q^{87} + 336 q^{88} - 1092 q^{89} + 864 q^{90} - 14140 q^{91} + 1344 q^{92} - 6468 q^{93} - 6288 q^{94} - 15576 q^{95} - 768 q^{96} - 14890 q^{97} + 10596 q^{98} + 25056 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(234))\)

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
234.4.a \(\chi_{234}(1, \cdot)\) 234.4.a.a 1 1
234.4.a.b 1
234.4.a.c 1
234.4.a.d 1
234.4.a.e 1
234.4.a.f 1
234.4.a.g 1
234.4.a.h 1
234.4.a.i 1
234.4.a.j 1
234.4.a.k 1
234.4.a.l 2
234.4.a.m 2
234.4.b \(\chi_{234}(181, \cdot)\) 234.4.b.a 2 1
234.4.b.b 4
234.4.b.c 4
234.4.b.d 8
234.4.e \(\chi_{234}(79, \cdot)\) 234.4.e.a 14 2
234.4.e.b 16
234.4.e.c 20
234.4.e.d 22
234.4.f \(\chi_{234}(133, \cdot)\) 234.4.f.a 42 2
234.4.f.b 42
234.4.g \(\chi_{234}(61, \cdot)\) 234.4.g.a 42 2
234.4.g.b 42
234.4.h \(\chi_{234}(55, \cdot)\) 234.4.h.a 2 2
234.4.h.b 2
234.4.h.c 2
234.4.h.d 2
234.4.h.e 4
234.4.h.f 4
234.4.h.g 4
234.4.h.h 4
234.4.h.i 4
234.4.h.j 6
234.4.j \(\chi_{234}(125, \cdot)\) 234.4.j.a 12 2
234.4.j.b 16
234.4.l \(\chi_{234}(127, \cdot)\) 234.4.l.a 4 2
234.4.l.b 8
234.4.l.c 8
234.4.l.d 16
234.4.p \(\chi_{234}(43, \cdot)\) 234.4.p.a 84 2
234.4.s \(\chi_{234}(121, \cdot)\) 234.4.s.a 84 2
234.4.t \(\chi_{234}(25, \cdot)\) 234.4.t.a 84 2
234.4.x \(\chi_{234}(71, \cdot)\) 234.4.x.a 24 4
234.4.x.b 32
234.4.y \(\chi_{234}(11, \cdot)\) 234.4.y.a 168 4
234.4.z \(\chi_{234}(41, \cdot)\) 234.4.z.a 168 4
234.4.bd \(\chi_{234}(5, \cdot)\) 234.4.bd.a 168 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(234))\) into lower level spaces

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