Properties

Label 1001.2.d
Level 1001
Weight 2
Character orbit d
Rep. character \(\chi_{1001}(155,\cdot)\)
Character field \(\Q\)
Dimension 72
Newform subspaces 3
Sturm bound 224
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1001.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1001, [\chi])\).

Total New Old
Modular forms 116 72 44
Cusp forms 108 72 36
Eisenstein series 8 0 8

Trace form

\( 72q - 76q^{4} + 80q^{9} + O(q^{10}) \) \( 72q - 76q^{4} + 80q^{9} - 16q^{10} + 24q^{12} - 4q^{13} + 8q^{14} + 84q^{16} + 24q^{17} + 4q^{22} - 12q^{23} - 84q^{25} - 8q^{26} + 48q^{27} - 12q^{29} - 16q^{30} - 4q^{35} - 124q^{36} + 8q^{38} + 48q^{40} + 8q^{42} + 20q^{43} + 80q^{48} - 72q^{49} - 8q^{51} - 20q^{52} + 12q^{53} - 24q^{56} - 56q^{61} + 48q^{62} - 124q^{64} + 28q^{65} - 176q^{68} - 16q^{69} - 40q^{75} - 8q^{77} + 24q^{78} - 4q^{79} + 168q^{81} + 176q^{82} - 24q^{87} - 36q^{88} - 152q^{90} - 8q^{91} + 40q^{92} - 8q^{94} + 36q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1001, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1001.2.d.a \(2\) \(7.993\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+iq^{2}-2q^{3}+q^{4}-2iq^{5}-2iq^{6}+\cdots\)
1001.2.d.b \(30\) \(7.993\) None \(0\) \(-8\) \(0\) \(0\)
1001.2.d.c \(40\) \(7.993\) None \(0\) \(12\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1001, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 3 T^{2} + 4 T^{4} \))
$3$ (\( ( 1 + 2 T + 3 T^{2} )^{2} \))
$5$ (\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))
$7$ (\( 1 + T^{2} \))
$11$ (\( 1 + T^{2} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))
$17$ (\( ( 1 - 2 T + 17 T^{2} )^{2} \))
$19$ (\( ( 1 - 19 T^{2} )^{2} \))
$23$ (\( ( 1 - 4 T + 23 T^{2} )^{2} \))
$29$ (\( ( 1 - 6 T + 29 T^{2} )^{2} \))
$31$ (\( ( 1 - 31 T^{2} )^{2} \))
$37$ (\( 1 - 58 T^{2} + 1369 T^{4} \))
$41$ (\( 1 + 62 T^{2} + 1681 T^{4} \))
$43$ (\( ( 1 - 10 T + 43 T^{2} )^{2} \))
$47$ (\( ( 1 - 47 T^{2} )^{2} \))
$53$ (\( ( 1 - 6 T + 53 T^{2} )^{2} \))
$59$ (\( 1 - 102 T^{2} + 3481 T^{4} \))
$61$ (\( ( 1 - 14 T + 61 T^{2} )^{2} \))
$67$ (\( 1 - 118 T^{2} + 4489 T^{4} \))
$71$ (\( 1 - 78 T^{2} + 5041 T^{4} \))
$73$ (\( ( 1 - 6 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))
$79$ (\( ( 1 - 2 T + 79 T^{2} )^{2} \))
$83$ (\( 1 - 150 T^{2} + 6889 T^{4} \))
$89$ (\( 1 + 146 T^{2} + 7921 T^{4} \))
$97$ (\( 1 - 158 T^{2} + 9409 T^{4} \))
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