Properties

Label 945.2.be
Level 945
Weight 2
Character orbit be
Rep. character \(\chi_{945}(206,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 64
Newform subspaces 3
Sturm bound 288
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

Total New Old
Modular forms 312 64 248
Cusp forms 264 64 200
Eisenstein series 48 0 48

Trace form

\( 64q + 32q^{4} + 2q^{7} + O(q^{10}) \) \( 64q + 32q^{4} + 2q^{7} - 6q^{13} + 6q^{14} - 32q^{16} + 64q^{25} + 24q^{26} - 8q^{28} - 18q^{29} + 24q^{31} - 2q^{37} + 120q^{38} - 6q^{41} - 8q^{43} + 42q^{44} + 6q^{46} + 36q^{47} + 10q^{49} - 48q^{53} - 102q^{56} - 30q^{59} - 60q^{61} - 64q^{64} - 6q^{65} + 14q^{67} + 60q^{68} + 6q^{70} + 54q^{77} - 4q^{79} - 60q^{83} - 6q^{85} + 42q^{89} - 6q^{91} - 12q^{92} - 6q^{97} + 54q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
945.2.be.a \(2\) \(7.546\) \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(-2\) \(-5\) \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
945.2.be.b \(30\) \(7.546\) None \(-3\) \(0\) \(-30\) \(6\)
945.2.be.c \(32\) \(7.546\) None \(0\) \(0\) \(32\) \(1\)

Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4} \))
$3$ 1
$5$ (\( ( 1 + T )^{2} \))
$7$ (\( 1 + 5 T + 7 T^{2} \))
$11$ (\( 1 - 10 T^{2} + 121 T^{4} \))
$13$ (\( ( 1 + 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))
$17$ (\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))
$19$ (\( 1 + 19 T^{2} + 361 T^{4} \))
$23$ (\( 1 - 19 T^{2} + 529 T^{4} \))
$29$ (\( 1 + 29 T^{2} + 841 T^{4} \))
$31$ (\( 1 + 6 T + 43 T^{2} + 186 T^{3} + 961 T^{4} \))
$37$ (\( 1 - 2 T - 33 T^{2} - 74 T^{3} + 1369 T^{4} \))
$41$ (\( 1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4} \))
$43$ (\( 1 + T - 42 T^{2} + 43 T^{3} + 1849 T^{4} \))
$47$ (\( 1 + 9 T + 34 T^{2} + 423 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 6 T + 65 T^{2} - 318 T^{3} + 2809 T^{4} \))
$59$ (\( 1 - 59 T^{2} + 3481 T^{4} \))
$61$ (\( 1 + 21 T + 208 T^{2} + 1281 T^{3} + 3721 T^{4} \))
$67$ (\( ( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))
$71$ (\( 1 - 94 T^{2} + 5041 T^{4} \))
$73$ (\( 1 + 18 T + 181 T^{2} + 1314 T^{3} + 5329 T^{4} \))
$79$ (\( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} \))
$83$ (\( 1 + 12 T + 61 T^{2} + 996 T^{3} + 6889 T^{4} \))
$89$ (\( 1 - 15 T + 136 T^{2} - 1335 T^{3} + 7921 T^{4} \))
$97$ (\( 1 + 12 T + 145 T^{2} + 1164 T^{3} + 9409 T^{4} \))
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