Properties

Label 234.6
Level 234
Weight 6
Dimension 1969
Nonzero newspaces 15
Sturm bound 18144
Trace bound 11

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Defining parameters

Level: \( N \) = \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 15 \)
Sturm bound: \(18144\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(234))\).

Total New Old
Modular forms 7752 1969 5783
Cusp forms 7368 1969 5399
Eisenstein series 384 0 384

Trace form

\( 1969 q + 16 q^{2} - 18 q^{3} + 64 q^{4} + 84 q^{5} + 168 q^{6} + 952 q^{7} - 320 q^{8} - 1158 q^{9} + O(q^{10}) \) \( 1969 q + 16 q^{2} - 18 q^{3} + 64 q^{4} + 84 q^{5} + 168 q^{6} + 952 q^{7} - 320 q^{8} - 1158 q^{9} - 1068 q^{10} + 1734 q^{11} + 768 q^{12} + 4108 q^{13} + 3584 q^{14} - 5328 q^{15} - 9561 q^{17} - 5136 q^{18} - 2456 q^{19} + 3312 q^{20} + 22620 q^{21} + 8520 q^{22} + 21840 q^{23} - 1152 q^{24} - 17813 q^{25} - 17432 q^{26} - 36288 q^{27} - 28480 q^{28} - 753 q^{29} + 51648 q^{30} + 120512 q^{31} + 4096 q^{32} + 55602 q^{33} + 36024 q^{34} - 80376 q^{35} - 27360 q^{36} - 154357 q^{37} - 126136 q^{38} - 104448 q^{39} - 16128 q^{40} - 98595 q^{41} - 74208 q^{42} + 56026 q^{43} + 82368 q^{44} + 246912 q^{45} + 160320 q^{46} + 173700 q^{47} - 7680 q^{48} + 65996 q^{49} - 25820 q^{50} - 165882 q^{51} - 108176 q^{52} + 178224 q^{53} + 233208 q^{54} - 93444 q^{55} + 6656 q^{56} - 179334 q^{57} - 76332 q^{58} - 173658 q^{59} - 85248 q^{60} + 19919 q^{61} - 129808 q^{62} - 367944 q^{63} - 94208 q^{64} + 465747 q^{65} - 160128 q^{66} + 490246 q^{67} + 53712 q^{68} + 452736 q^{69} + 291024 q^{70} + 686760 q^{71} + 119424 q^{72} - 67952 q^{73} + 119060 q^{74} - 396114 q^{75} - 88160 q^{76} - 1422828 q^{77} - 240840 q^{78} - 1081096 q^{79} - 112896 q^{80} - 627198 q^{81} - 566316 q^{82} - 224304 q^{83} + 4032 q^{84} + 1127559 q^{85} + 705080 q^{86} + 1159068 q^{87} + 136320 q^{88} + 1192380 q^{89} + 689472 q^{90} + 1126516 q^{91} + 474816 q^{92} - 23232 q^{93} + 221280 q^{94} - 1701528 q^{95} - 24576 q^{96} - 1250254 q^{97} + 49080 q^{98} - 125172 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(234))\)

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
234.6.a \(\chi_{234}(1, \cdot)\) 234.6.a.a 1 1
234.6.a.b 1
234.6.a.c 1
234.6.a.d 1
234.6.a.e 1
234.6.a.f 1
234.6.a.g 1
234.6.a.h 2
234.6.a.i 2
234.6.a.j 2
234.6.a.k 2
234.6.a.l 2
234.6.a.m 2
234.6.a.n 3
234.6.a.o 3
234.6.b \(\chi_{234}(181, \cdot)\) 234.6.b.a 2 1
234.6.b.b 2
234.6.b.c 6
234.6.b.d 8
234.6.b.e 12
234.6.e \(\chi_{234}(79, \cdot)\) n/a 120 2
234.6.f \(\chi_{234}(133, \cdot)\) n/a 140 2
234.6.g \(\chi_{234}(61, \cdot)\) n/a 140 2
234.6.h \(\chi_{234}(55, \cdot)\) 234.6.h.a 4 2
234.6.h.b 4
234.6.h.c 6
234.6.h.d 6
234.6.h.e 6
234.6.h.f 8
234.6.h.g 12
234.6.h.h 12
234.6.j \(\chi_{234}(125, \cdot)\) 234.6.j.a 24 2
234.6.j.b 28
234.6.l \(\chi_{234}(127, \cdot)\) 234.6.l.a 12 2
234.6.l.b 12
234.6.l.c 12
234.6.l.d 20
234.6.p \(\chi_{234}(43, \cdot)\) n/a 140 2
234.6.s \(\chi_{234}(121, \cdot)\) n/a 140 2
234.6.t \(\chi_{234}(25, \cdot)\) n/a 140 2
234.6.x \(\chi_{234}(71, \cdot)\) 234.6.x.a 40 4
234.6.x.b 48
234.6.y \(\chi_{234}(11, \cdot)\) n/a 280 4
234.6.z \(\chi_{234}(41, \cdot)\) n/a 280 4
234.6.bd \(\chi_{234}(5, \cdot)\) n/a 280 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(234))\) into lower level spaces

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