Properties

Label 231.4
Level 231
Weight 4
Dimension 3980
Nonzero newspaces 16
Newform subspaces 34
Sturm bound 15360
Trace bound 3

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Defining parameters

Level: \( N \) = \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 34 \)
Sturm bound: \(15360\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(231))\).

Total New Old
Modular forms 6000 4156 1844
Cusp forms 5520 3980 1540
Eisenstein series 480 176 304

Trace form

\( 3980 q - 26 q^{3} - 28 q^{4} + 48 q^{5} - 48 q^{6} + 38 q^{7} + 52 q^{8} + 62 q^{9} + O(q^{10}) \) \( 3980 q - 26 q^{3} - 28 q^{4} + 48 q^{5} - 48 q^{6} + 38 q^{7} + 52 q^{8} + 62 q^{9} + 244 q^{10} + 200 q^{11} + 472 q^{12} + 208 q^{13} + 234 q^{14} - 274 q^{15} - 1308 q^{16} - 576 q^{17} - 840 q^{18} - 256 q^{19} - 188 q^{20} - 780 q^{21} + 1988 q^{22} + 1096 q^{23} + 1712 q^{24} + 1532 q^{25} + 688 q^{26} + 136 q^{27} + 1120 q^{28} - 104 q^{29} - 830 q^{30} - 1300 q^{31} - 1124 q^{32} - 2829 q^{33} - 3288 q^{34} - 1328 q^{35} - 3006 q^{36} - 2804 q^{37} - 2120 q^{38} - 304 q^{39} + 188 q^{40} + 4056 q^{41} - 2234 q^{42} - 2104 q^{43} - 644 q^{44} + 998 q^{45} + 2124 q^{46} + 776 q^{47} + 6222 q^{48} + 6622 q^{49} + 9376 q^{50} + 8208 q^{51} + 14100 q^{52} + 3560 q^{53} + 9366 q^{54} - 1820 q^{55} - 1740 q^{56} - 1440 q^{57} - 3716 q^{58} + 2712 q^{59} - 6050 q^{60} + 1204 q^{61} + 6936 q^{62} + 819 q^{63} - 1456 q^{64} + 2352 q^{65} - 7032 q^{66} - 6916 q^{67} - 8128 q^{68} - 6338 q^{69} - 10392 q^{70} - 13776 q^{71} - 11870 q^{72} - 13828 q^{73} - 15240 q^{74} - 11022 q^{75} - 26512 q^{76} - 12600 q^{77} - 4208 q^{78} - 4420 q^{79} - 24972 q^{80} - 5794 q^{81} - 536 q^{82} + 920 q^{83} - 11562 q^{84} + 14404 q^{85} + 6628 q^{86} + 12198 q^{87} + 44492 q^{88} + 20104 q^{89} + 12370 q^{90} + 20262 q^{91} + 26668 q^{92} + 6666 q^{93} + 452 q^{94} + 6072 q^{95} - 7550 q^{96} - 12580 q^{97} + 6904 q^{98} - 5344 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(231))\)

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
231.4.a \(\chi_{231}(1, \cdot)\) 231.4.a.a 1 1
231.4.a.b 1
231.4.a.c 1
231.4.a.d 1
231.4.a.e 1
231.4.a.f 2
231.4.a.g 2
231.4.a.h 2
231.4.a.i 2
231.4.a.j 5
231.4.a.k 5
231.4.a.l 5
231.4.c \(\chi_{231}(76, \cdot)\) 231.4.c.a 48 1
231.4.e \(\chi_{231}(188, \cdot)\) 231.4.e.a 80 1
231.4.g \(\chi_{231}(197, \cdot)\) 231.4.g.a 72 1
231.4.i \(\chi_{231}(67, \cdot)\) 231.4.i.a 16 2
231.4.i.b 20
231.4.i.c 20
231.4.i.d 24
231.4.j \(\chi_{231}(64, \cdot)\) 231.4.j.a 28 4
231.4.j.b 36
231.4.j.c 36
231.4.j.d 44
231.4.l \(\chi_{231}(32, \cdot)\) 231.4.l.a 184 2
231.4.n \(\chi_{231}(89, \cdot)\) 231.4.n.a 160 2
231.4.p \(\chi_{231}(10, \cdot)\) 231.4.p.a 96 2
231.4.s \(\chi_{231}(8, \cdot)\) 231.4.s.a 288 4
231.4.u \(\chi_{231}(20, \cdot)\) 231.4.u.a 368 4
231.4.w \(\chi_{231}(13, \cdot)\) 231.4.w.a 192 4
231.4.y \(\chi_{231}(4, \cdot)\) 231.4.y.a 192 8
231.4.y.b 192
231.4.ba \(\chi_{231}(19, \cdot)\) 231.4.ba.a 384 8
231.4.bc \(\chi_{231}(5, \cdot)\) 231.4.bc.a 736 8
231.4.be \(\chi_{231}(2, \cdot)\) 231.4.be.a 736 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(231))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(231)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 1}\)