Properties

Label 12.7.c
Level 12
Weight 7
Character orbit c
Rep. character \(\chi_{12}(5,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 14
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 12.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(12, [\chi])\).

Total New Old
Modular forms 15 2 13
Cusp forms 9 2 7
Eisenstein series 6 0 6

Trace form

\( 2q - 6q^{3} + 484q^{7} - 1422q^{9} + O(q^{10}) \) \( 2q - 6q^{3} + 484q^{7} - 1422q^{9} + 5236q^{13} - 8640q^{15} + 11572q^{19} - 1452q^{21} - 20590q^{25} + 12906q^{27} - 40892q^{31} + 95040q^{33} - 93548q^{37} - 15708q^{39} + 137236q^{43} + 51840q^{45} - 118170q^{49} - 380160q^{51} + 570240q^{55} - 34716q^{57} + 49588q^{61} - 344124q^{63} - 168716q^{67} + 501120q^{69} - 227612q^{73} + 61770q^{75} - 319484q^{79} + 959202q^{81} - 2280960q^{85} + 665280q^{87} + 1267112q^{91} + 122676q^{93} + 1799044q^{97} - 570240q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.7.c.a \(2\) \(2.761\) \(\Q(\sqrt{-5}) \) None \(0\) \(-6\) \(0\) \(484\) \(q+(-3+\beta )q^{3}+6\beta q^{5}+242q^{7}+(-711+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 + 6 T + 729 T^{2} \)
$5$ \( 1 - 5330 T^{2} + 244140625 T^{4} \)
$7$ \( ( 1 - 242 T + 117649 T^{2} )^{2} \)
$11$ \( 1 - 406802 T^{2} + 3138428376721 T^{4} \)
$13$ \( ( 1 - 2618 T + 4826809 T^{2} )^{2} \)
$17$ \( 1 + 1905982 T^{2} + 582622237229761 T^{4} \)
$19$ \( ( 1 - 5786 T + 47045881 T^{2} )^{2} \)
$23$ \( 1 - 208876898 T^{2} + 21914624432020321 T^{4} \)
$29$ \( 1 - 1035966962 T^{2} + 353814783205469041 T^{4} \)
$31$ \( ( 1 + 20446 T + 887503681 T^{2} )^{2} \)
$37$ \( ( 1 + 46774 T + 2565726409 T^{2} )^{2} \)
$41$ \( 1 - 9487663202 T^{2} + 22563490300366186081 T^{4} \)
$43$ \( ( 1 - 68618 T + 6321363049 T^{2} )^{2} \)
$47$ \( 1 - 21106800578 T^{2} + \)\(11\!\cdots\!41\)\( T^{4} \)
$53$ \( 1 - 14819087378 T^{2} + \)\(49\!\cdots\!41\)\( T^{4} \)
$59$ \( 1 - 61991044562 T^{2} + \)\(17\!\cdots\!81\)\( T^{4} \)
$61$ \( ( 1 - 24794 T + 51520374361 T^{2} )^{2} \)
$67$ \( ( 1 + 84358 T + 90458382169 T^{2} )^{2} \)
$71$ \( 1 - 151063967522 T^{2} + \)\(16\!\cdots\!41\)\( T^{4} \)
$73$ \( ( 1 + 113806 T + 151334226289 T^{2} )^{2} \)
$79$ \( ( 1 + 159742 T + 243087455521 T^{2} )^{2} \)
$83$ \( 1 - 388294032818 T^{2} + \)\(10\!\cdots\!61\)\( T^{4} \)
$89$ \( 1 + 583819025758 T^{2} + \)\(24\!\cdots\!21\)\( T^{4} \)
$97$ \( ( 1 - 899522 T + 832972004929 T^{2} )^{2} \)
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