Properties

Label 1512.2.q
Level 1512
Weight 2
Character orbit q
Rep. character \(\chi_{1512}(793,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 48
Newform subspaces 4
Sturm bound 576
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 624 48 576
Cusp forms 528 48 480
Eisenstein series 96 0 96

Trace form

\( 48q - 4q^{5} + O(q^{10}) \) \( 48q - 4q^{5} - 8q^{17} + 4q^{23} - 24q^{25} + 6q^{29} - 12q^{31} - 12q^{35} - 18q^{41} + 6q^{43} + 12q^{47} - 6q^{49} - 4q^{53} + 12q^{55} - 72q^{59} - 12q^{61} + 24q^{65} + 40q^{71} - 28q^{77} + 12q^{79} + 36q^{83} - 18q^{89} - 6q^{91} - 20q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1512.2.q.a \(2\) \(12.073\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-4\) \(q+(-1+\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
1512.2.q.b \(2\) \(12.073\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(4\) \(q+(1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots\)
1512.2.q.c \(22\) \(12.073\) None \(0\) \(0\) \(-3\) \(-5\)
1512.2.q.d \(22\) \(12.073\) None \(0\) \(0\) \(-1\) \(5\)

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( \))(\( \))
$3$ (\( \))(\( \))
$5$ (\( 1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4} \))(\( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))
$11$ (\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))
$13$ (\( 1 + 3 T - 4 T^{2} + 39 T^{3} + 169 T^{4} \))(\( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} \))
$17$ (\( 1 + 5 T + 8 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))
$19$ (\( ( 1 - T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))
$23$ (\( 1 - 5 T + 2 T^{2} - 115 T^{3} + 529 T^{4} \))(\( 1 - T - 22 T^{2} - 23 T^{3} + 529 T^{4} \))
$29$ (\( 1 + T - 28 T^{2} + 29 T^{3} + 841 T^{4} \))(\( 1 - 9 T + 52 T^{2} - 261 T^{3} + 841 T^{4} \))
$31$ (\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))
$37$ (\( 1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4} \))(\( 1 + 5 T - 12 T^{2} + 185 T^{3} + 1369 T^{4} \))
$41$ (\( 1 + 5 T - 16 T^{2} + 205 T^{3} + 1681 T^{4} \))(\( 1 - 7 T + 8 T^{2} - 287 T^{3} + 1681 T^{4} \))
$43$ (\( 1 - 7 T + 6 T^{2} - 301 T^{3} + 1849 T^{4} \))(\( 1 + 3 T - 34 T^{2} + 129 T^{3} + 1849 T^{4} \))
$47$ (\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))
$53$ (\( 1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4} \))(\( 1 - 9 T + 28 T^{2} - 477 T^{3} + 2809 T^{4} \))
$59$ (\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))
$61$ (\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))
$67$ (\( ( 1 + 12 T + 67 T^{2} )^{2} \))(\( ( 1 - 12 T + 67 T^{2} )^{2} \))
$71$ (\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))
$73$ (\( 1 - 5 T - 48 T^{2} - 365 T^{3} + 5329 T^{4} \))(\( 1 - 13 T + 96 T^{2} - 949 T^{3} + 5329 T^{4} \))
$79$ (\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))
$83$ (\( 1 + 15 T + 142 T^{2} + 1245 T^{3} + 6889 T^{4} \))(\( 1 + 13 T + 86 T^{2} + 1079 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 5 T - 64 T^{2} + 445 T^{3} + 7921 T^{4} \))(\( 1 + 9 T - 8 T^{2} + 801 T^{3} + 7921 T^{4} \))
$97$ (\( 1 + 7 T - 48 T^{2} + 679 T^{3} + 9409 T^{4} \))(\( 1 - 17 T + 192 T^{2} - 1649 T^{3} + 9409 T^{4} \))
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