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Properties

Label 6.31
Level 6
Weight 31
Dimension 10
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 62
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 31 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(62\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{31}(\Gamma_1(6))\).

Total New Old
Modular forms 32 10 22
Cusp forms 28 10 18
Eisenstein series 4 0 4

Trace form

\( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9} + O(q^{10}) \) \( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9} - 1111538175836160 q^{10} - 7591226920402944 q^{12} + 11241857908456580 q^{13} - 1208370750576105600 q^{15} + 2882303761517117440 q^{16} + 4378961453216956416 q^{18} - 406434941012438620 q^{19} + 189341373476724706020 q^{21} - 175966920878069907456 q^{22} + 78269746773932113920 q^{24} - 538750688835772733030 q^{25} - 509686212259700532126 q^{27} + 783474298257252810752 q^{28} + 3618734882327478927360 q^{30} - 3850790055930904811020 q^{31} + 13877514934601873876352 q^{33} - 21974427701517892976640 q^{34} - 22394560921038760181760 q^{36} + 691786417224189171658916 q^{37} + 264189297409049008449300 q^{39} + 596752514183975581777920 q^{40} + 2551733261187619598893056 q^{42} - 10594373354873893550389372 q^{43} + 21961398854703004532478720 q^{45} - 14905926072892021549301760 q^{46} + 4075508919955679952764928 q^{48} - 14303693611422252234715650 q^{49} + 100757981401326611204590080 q^{51} - 6035426507887496617000960 q^{52} + 186364360915292902942310400 q^{54} - 905529883473273884900970240 q^{55} + 1357830109447011748343825076 q^{57} - 1026862318649343581985177600 q^{58} + 648739106895918338880307200 q^{60} - 2949272535924647913201299260 q^{61} + 5088794127795653673352888692 q^{63} - 1547425049106725343623905280 q^{64} + 3787402697011447732654571520 q^{66} - 10556251754234326335356822044 q^{67} + 15764240424701154050198334720 q^{69} - 8691440888931957213379952640 q^{70} - 2350937029001432724922171392 q^{72} + 12106003505184711607130189300 q^{73} - 7500206691267464218185712830 q^{75} + 218203097450014125263421440 q^{76} - 23839067108381696719249735680 q^{78} + 68719005124237783442983312820 q^{79} - 111620808361643664456575921430 q^{81} + 18283730424263848186657898496 q^{82} - 101651875857781803693889290240 q^{84} + 403836274868708986530058828800 q^{85} - 512433611792960206983797969280 q^{87} + 94471521293641232015658319872 q^{88} - 426164288449255115819581440000 q^{90} + 1222541373056582384854822798600 q^{91} - 983623123086267594817934884284 q^{93} - 80746046881825464175401369600 q^{94} - 42020750332529991826318295040 q^{96} - 1391585232259866867438139103212 q^{97} + 2707446209006624257844338302720 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{31}^{\mathrm{new}}(\Gamma_1(6))\)

We only show spaces with odd 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
6.31.b \(\chi_{6}(5, \cdot)\) 6.31.b.a 10 1

Decomposition of \(S_{31}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{31}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{31}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)