Properties

Label 6.7
Level 6
Weight 7
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 14
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6\( 6 = 2 \cdot 3 \) \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(6))\).

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

Trace form

\( 2q + 42q^{3} - 64q^{4} - 192q^{6} + 4q^{7} + 306q^{9} + O(q^{10}) \) \( 2q + 42q^{3} - 64q^{4} - 192q^{6} + 4q^{7} + 306q^{9} + 1920q^{10} - 1344q^{12} - 5900q^{13} + 5760q^{15} + 2048q^{16} - 8064q^{18} + 10516q^{19} + 84q^{21} + 384q^{22} + 6144q^{24} - 26350q^{25} - 17766q^{27} - 128q^{28} + 40320q^{30} + 45796q^{31} + 1152q^{33} - 50688q^{34} - 9792q^{36} + 68116q^{37} - 123900q^{39} - 61440q^{40} - 384q^{42} - 12812q^{43} + 241920q^{45} + 115968q^{46} + 43008q^{48} - 235290q^{49} - 152064q^{51} + 188800q^{52} - 198720q^{54} - 11520q^{55} + 220836q^{57} - 24960q^{58} - 184320q^{60} - 125132q^{61} + 612q^{63} - 65536q^{64} + 8064q^{66} + 877396q^{67} + 347904q^{69} + 3840q^{70} + 258048q^{72} - 1461020q^{73} - 553350q^{75} - 336512q^{76} + 566400q^{78} + 681124q^{79} - 969246q^{81} + 189696q^{82} - 2688q^{84} + 1520640q^{85} - 74880q^{87} - 12288q^{88} + 293760q^{90} - 11800q^{91} + 961716q^{93} - 2035200q^{94} - 196608q^{96} - 562172q^{97} + 48384q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)

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
6.7.b \(\chi_{6}(5, \cdot)\) 6.7.b.a 2 1

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 32 T^{2} \)
$3$ \( 1 - 42 T + 729 T^{2} \)
$5$ \( 1 - 2450 T^{2} + 244140625 T^{4} \)
$7$ \( ( 1 - 2 T + 117649 T^{2} )^{2} \)
$11$ \( 1 - 3541970 T^{2} + 3138428376721 T^{4} \)
$13$ \( ( 1 + 2950 T + 4826809 T^{2} )^{2} \)
$17$ \( 1 - 28202690 T^{2} + 582622237229761 T^{4} \)
$19$ \( ( 1 - 5258 T + 47045881 T^{2} )^{2} \)
$23$ \( 1 - 191004770 T^{2} + 21914624432020321 T^{4} \)
$29$ \( 1 - 1184779442 T^{2} + 353814783205469041 T^{4} \)
$31$ \( ( 1 - 22898 T + 887503681 T^{2} )^{2} \)
$37$ \( ( 1 - 34058 T + 2565726409 T^{2} )^{2} \)
$41$ \( 1 - 9219079010 T^{2} + 22563490300366186081 T^{4} \)
$43$ \( ( 1 + 6406 T + 6321363049 T^{2} )^{2} \)
$47$ \( 1 + 10801249342 T^{2} + \)\(11\!\cdots\!41\)\( T^{4} \)
$53$ \( 1 - 7253988050 T^{2} + \)\(49\!\cdots\!41\)\( T^{4} \)
$59$ \( 1 + 22449655150 T^{2} + \)\(17\!\cdots\!81\)\( T^{4} \)
$61$ \( ( 1 + 62566 T + 51520374361 T^{2} )^{2} \)
$67$ \( ( 1 - 438698 T + 90458382169 T^{2} )^{2} \)
$71$ \( 1 - 251546372642 T^{2} + \)\(16\!\cdots\!41\)\( T^{4} \)
$73$ \( ( 1 + 730510 T + 151334226289 T^{2} )^{2} \)
$79$ \( ( 1 - 340562 T + 243087455521 T^{2} )^{2} \)
$83$ \( 1 - 407613512306 T^{2} + \)\(10\!\cdots\!61\)\( T^{4} \)
$89$ \( 1 - 844406214050 T^{2} + \)\(24\!\cdots\!21\)\( T^{4} \)
$97$ \( ( 1 + 281086 T + 832972004929 T^{2} )^{2} \)
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