Properties

Label 231.8
Level 231
Weight 8
Dimension 9408
Nonzero newspaces 16
Sturm bound 30720
Trace bound 3

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Defining parameters

Level: \( N \) = \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(30720\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(231))\).

Total New Old
Modular forms 13680 9584 4096
Cusp forms 13200 9408 3792
Eisenstein series 480 176 304

Trace form

\( 9408 q + 24 q^{2} - 68 q^{3} - 1420 q^{4} + 1548 q^{5} + 5364 q^{6} - 808 q^{7} - 30508 q^{8} + 11708 q^{9} + O(q^{10}) \) \( 9408 q + 24 q^{2} - 68 q^{3} - 1420 q^{4} + 1548 q^{5} + 5364 q^{6} - 808 q^{7} - 30508 q^{8} + 11708 q^{9} + 12964 q^{10} + 13786 q^{11} + 18904 q^{12} - 51856 q^{13} - 11742 q^{14} + 49886 q^{15} + 61604 q^{16} - 89484 q^{17} - 256116 q^{18} - 3744 q^{19} + 1351652 q^{20} + 230526 q^{21} + 460244 q^{22} - 648376 q^{23} - 891856 q^{24} - 830708 q^{25} - 443440 q^{26} + 706222 q^{27} + 1573056 q^{28} + 1142744 q^{29} + 185530 q^{30} - 2946652 q^{31} - 6235780 q^{32} - 962898 q^{33} + 6758328 q^{34} + 3622772 q^{35} + 2766186 q^{36} - 335648 q^{37} - 5222584 q^{38} - 5047282 q^{39} - 8785732 q^{40} - 1139088 q^{41} - 7631342 q^{42} + 9552880 q^{43} + 24711788 q^{44} + 18877658 q^{45} + 4607788 q^{46} - 11786072 q^{47} - 16271250 q^{48} - 18986340 q^{49} - 23037784 q^{50} - 13855218 q^{51} + 5501652 q^{52} + 18529660 q^{53} + 16164654 q^{54} + 34223600 q^{55} + 25992756 q^{56} + 25381932 q^{57} + 3218268 q^{58} - 541188 q^{59} - 5134850 q^{60} - 30342132 q^{61} - 85437960 q^{62} - 58781136 q^{63} - 98678384 q^{64} - 17091528 q^{65} - 4508400 q^{66} + 94567648 q^{67} + 146255680 q^{68} + 56519566 q^{69} + 126971848 q^{70} - 2020704 q^{71} + 59906242 q^{72} + 51741720 q^{73} - 4852872 q^{74} - 5298522 q^{75} - 169161904 q^{76} - 77755902 q^{77} - 159206624 q^{78} - 165437524 q^{79} - 192916812 q^{80} + 12853460 q^{81} + 34701008 q^{82} + 97410424 q^{83} + 135602166 q^{84} + 219072424 q^{85} + 159622292 q^{86} + 61676832 q^{87} + 223159596 q^{88} - 8288872 q^{89} - 84154550 q^{90} - 116038964 q^{91} - 158804308 q^{92} + 94880694 q^{93} + 159604340 q^{94} + 134840892 q^{95} + 33001570 q^{96} - 193771992 q^{97} - 26466640 q^{98} - 195846010 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(231))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
231.8.a \(\chi_{231}(1, \cdot)\) 231.8.a.a 7 1
231.8.a.b 7
231.8.a.c 7
231.8.a.d 7
231.8.a.e 10
231.8.a.f 10
231.8.a.g 10
231.8.a.h 10
231.8.c \(\chi_{231}(76, \cdot)\) n/a 112 1
231.8.e \(\chi_{231}(188, \cdot)\) n/a 188 1
231.8.g \(\chi_{231}(197, \cdot)\) n/a 168 1
231.8.i \(\chi_{231}(67, \cdot)\) n/a 188 2
231.8.j \(\chi_{231}(64, \cdot)\) n/a 336 4
231.8.l \(\chi_{231}(32, \cdot)\) n/a 440 2
231.8.n \(\chi_{231}(89, \cdot)\) n/a 372 2
231.8.p \(\chi_{231}(10, \cdot)\) n/a 224 2
231.8.s \(\chi_{231}(8, \cdot)\) n/a 672 4
231.8.u \(\chi_{231}(20, \cdot)\) n/a 880 4
231.8.w \(\chi_{231}(13, \cdot)\) n/a 448 4
231.8.y \(\chi_{231}(4, \cdot)\) n/a 896 8
231.8.ba \(\chi_{231}(19, \cdot)\) n/a 896 8
231.8.bc \(\chi_{231}(5, \cdot)\) n/a 1760 8
231.8.be \(\chi_{231}(2, \cdot)\) n/a 1760 8

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(231))\) into lower level spaces

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