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Properties

Label 6.29
Level 6
Weight 29
Dimension 10
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 58
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 29 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(58\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{29}(\Gamma_1(6))\).

Total New Old
Modular forms 30 10 20
Cusp forms 26 10 16
Eisenstein series 4 0 4

Trace form

\( 10 q - 8805966 q^{3} - 1342177280 q^{4} - 105213788160 q^{6} - 640581497308 q^{7} + 27322446020490 q^{9} + O(q^{10}) \) \( 10 q - 8805966 q^{3} - 1342177280 q^{4} - 105213788160 q^{6} - 640581497308 q^{7} + 27322446020490 q^{9} - 27967405817856 q^{10} + 1181916749365248 q^{12} - 12482103411068620 q^{13} + 61319980558590048 q^{15} + 180143985094819840 q^{16} - 211642157524451328 q^{18} + 1498633795842086180 q^{19} - 2708280323934164940 q^{21} + 1023106116785405952 q^{22} + 14121555601108500480 q^{24} - 118736693316812330006 q^{25} - 129985199891557730478 q^{27} + 85977393167517876224 q^{28} - 714377425121915830272 q^{30} - 1023485060491138610140 q^{31} - 810380893747609058976 q^{33} - 3702565864316094382080 q^{34} - 3667156628272809246720 q^{36} - 15135414444725138913292 q^{37} - 90527454224201364861180 q^{39} + 3753721666926614151168 q^{40} - 83782317508213524529152 q^{42} + 197073485543953049687396 q^{43} - 353765338722291397174848 q^{45} + 360592317150577993973760 q^{46} - 158634180784949028716544 q^{48} + 3984185807056499345366430 q^{49} - 4562801433917127503049600 q^{51} + 1675319560494680228495360 q^{52} - 6215034612836859467857920 q^{54} + 16657974515766806205279552 q^{55} - 11868576742254344957945292 q^{57} + 6219704509741016298946560 q^{58} - 8230228471578127125970944 q^{60} + 26578327776203381143621940 q^{61} - 61528988659547989966678236 q^{63} - 24178516392292583494123520 q^{64} - 30776817485090369488158720 q^{66} - 16154878707937381443394972 q^{67} + 181226188204376873380361280 q^{69} - 257896094107734027347951616 q^{70} + 28406129531949961690742784 q^{72} - 331445702470743781613732140 q^{73} + 1054668864238007063534780178 q^{75} - 201143223181940653859799040 q^{76} + 415048527147123554842705920 q^{78} + 264192536445434377129602980 q^{79} + 1925492182685962075308092490 q^{81} - 1026212980364810668034752512 q^{82} + 363499231865547639824056320 q^{84} - 2969528244247922277988161792 q^{85} + 341427023984652036115514400 q^{87} - 137318978497839850435117056 q^{88} - 3202489169155688742678822912 q^{90} + 4475257581880995451850106760 q^{91} - 23261530114293985837100615628 q^{93} + 6585642783869668160671580160 q^{94} - 1895363108606457215912509440 q^{96} + 25466607638754754885505536724 q^{97} - 23060446172911946696379370560 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{29}^{\mathrm{new}}(\Gamma_1(6))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6.29.b \(\chi_{6}(5, \cdot)\) 6.29.b.a 10 1

Decomposition of \(S_{29}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{29}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{29}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)