Properties

Label 3.7
Level 3
Weight 7
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3\( 3 \) \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(3))\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\( q - 27q^{3} + 64q^{4} - 286q^{7} + 729q^{9} + O(q^{10}) \) \( q - 27q^{3} + 64q^{4} - 286q^{7} + 729q^{9} - 1728q^{12} + 506q^{13} + 4096q^{16} - 10582q^{19} + 7722q^{21} + 15625q^{25} - 19683q^{27} - 18304q^{28} + 35282q^{31} + 46656q^{36} - 89206q^{37} - 13662q^{39} + 111386q^{43} - 110592q^{48} - 35853q^{49} + 32384q^{52} + 285714q^{57} - 420838q^{61} - 208494q^{63} + 262144q^{64} + 172874q^{67} + 638066q^{73} - 421875q^{75} - 677248q^{76} - 204622q^{79} + 531441q^{81} + 494208q^{84} - 144716q^{91} - 952614q^{93} - 56446q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.7.b \(\chi_{3}(2, \cdot)\) 3.7.b.a 1 1

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - 8 T )( 1 + 8 T ) \)
$3$ \( 1 + 27 T \)
$5$ \( ( 1 - 125 T )( 1 + 125 T ) \)
$7$ \( 1 + 286 T + 117649 T^{2} \)
$11$ \( ( 1 - 1331 T )( 1 + 1331 T ) \)
$13$ \( 1 - 506 T + 4826809 T^{2} \)
$17$ \( ( 1 - 4913 T )( 1 + 4913 T ) \)
$19$ \( 1 + 10582 T + 47045881 T^{2} \)
$23$ \( ( 1 - 12167 T )( 1 + 12167 T ) \)
$29$ \( ( 1 - 24389 T )( 1 + 24389 T ) \)
$31$ \( 1 - 35282 T + 887503681 T^{2} \)
$37$ \( 1 + 89206 T + 2565726409 T^{2} \)
$41$ \( ( 1 - 68921 T )( 1 + 68921 T ) \)
$43$ \( 1 - 111386 T + 6321363049 T^{2} \)
$47$ \( ( 1 - 103823 T )( 1 + 103823 T ) \)
$53$ \( ( 1 - 148877 T )( 1 + 148877 T ) \)
$59$ \( ( 1 - 205379 T )( 1 + 205379 T ) \)
$61$ \( 1 + 420838 T + 51520374361 T^{2} \)
$67$ \( 1 - 172874 T + 90458382169 T^{2} \)
$71$ \( ( 1 - 357911 T )( 1 + 357911 T ) \)
$73$ \( 1 - 638066 T + 151334226289 T^{2} \)
$79$ \( 1 + 204622 T + 243087455521 T^{2} \)
$83$ \( ( 1 - 571787 T )( 1 + 571787 T ) \)
$89$ \( ( 1 - 704969 T )( 1 + 704969 T ) \)
$97$ \( 1 + 56446 T + 832972004929 T^{2} \)
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