Properties

Label 1005.2.c
Level 1005
Weight 2
Character orbit c
Rep. character \(\chi_{1005}(604,\cdot)\)
Character field \(\Q\)
Dimension 68
Newform subspaces 4
Sturm bound 272
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1005 = 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1005.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(272\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1005, [\chi])\).

Total New Old
Modular forms 140 68 72
Cusp forms 132 68 64
Eisenstein series 8 0 8

Trace form

\( 68q - 68q^{4} - 68q^{9} + O(q^{10}) \) \( 68q - 68q^{4} - 68q^{9} - 12q^{10} + 24q^{14} - 4q^{15} + 68q^{16} + 8q^{20} + 8q^{21} - 4q^{25} - 40q^{26} - 8q^{29} - 16q^{30} + 40q^{34} + 20q^{35} + 68q^{36} - 16q^{39} + 28q^{40} - 16q^{41} - 48q^{44} + 40q^{46} - 92q^{49} + 8q^{50} - 8q^{51} + 48q^{55} + 16q^{59} - 8q^{60} - 16q^{61} - 44q^{64} + 52q^{65} - 8q^{66} + 16q^{69} - 64q^{70} - 32q^{71} - 8q^{74} + 24q^{75} - 32q^{76} - 32q^{79} - 32q^{80} + 68q^{81} - 8q^{85} - 16q^{86} - 16q^{89} + 12q^{90} + 8q^{91} + 8q^{94} - 16q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1005, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1005.2.c.a \(2\) \(8.025\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
1005.2.c.b \(4\) \(8.025\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{2}+\beta _{2}q^{3}-4q^{4}+(-1+\cdots)q^{5}+\cdots\)
1005.2.c.c \(28\) \(8.025\) None \(0\) \(0\) \(0\) \(0\)
1005.2.c.d \(34\) \(8.025\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1005, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1005, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 3 T^{2} + 4 T^{4} \))(\( ( 1 + 2 T^{2} + 4 T^{4} )^{2} \))
$3$ (\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))
$5$ (\( 1 - 4 T + 5 T^{2} \))(\( 1 + 4 T + 8 T^{2} + 20 T^{3} + 25 T^{4} \))
$7$ (\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 - 8 T^{2} + 49 T^{4} )^{2} \))
$11$ (\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{4} \))
$13$ (\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 20 T^{2} + 169 T^{4} )^{2} \))
$17$ (\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 - 54 T^{2} + 1283 T^{4} - 15606 T^{6} + 83521 T^{8} \))
$19$ (\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{4} \))
$23$ (\( 1 - 42 T^{2} + 529 T^{4} \))(\( 1 - 62 T^{2} + 1803 T^{4} - 32798 T^{6} + 279841 T^{8} \))
$29$ (\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 10 T + 77 T^{2} + 290 T^{3} + 841 T^{4} )^{2} \))
$31$ (\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 54 T^{2} + 248 T^{3} + 961 T^{4} )^{2} \))
$37$ (\( ( 1 - 37 T^{2} )^{2} \))(\( 1 - 82 T^{2} + 3555 T^{4} - 112258 T^{6} + 1874161 T^{8} \))
$41$ (\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 112 T^{2} + 492 T^{3} + 1681 T^{4} )^{2} \))
$43$ (\( 1 + 58 T^{2} + 1849 T^{4} \))(\( ( 1 - 50 T^{2} + 1849 T^{4} )^{2} \))
$47$ (\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 4763 T^{4} - 172302 T^{6} + 4879681 T^{8} \))
$53$ (\( 1 - 6 T^{2} + 2809 T^{4} \))(\( ( 1 - 52 T^{2} + 2809 T^{4} )^{2} \))
$59$ (\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 6 T + 121 T^{2} + 354 T^{3} + 3481 T^{4} )^{2} \))
$61$ (\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 4 T + 72 T^{2} - 244 T^{3} + 3721 T^{4} )^{2} \))
$67$ (\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))
$71$ (\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 118 T^{2} + 5041 T^{4} )^{2} \))
$73$ (\( 1 - 82 T^{2} + 5329 T^{4} \))(\( 1 - 146 T^{2} + 11283 T^{4} - 778034 T^{6} + 28398241 T^{8} \))
$79$ (\( ( 1 + 2 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 150 T^{2} + 632 T^{3} + 6241 T^{4} )^{2} \))
$83$ (\( 1 + 30 T^{2} + 6889 T^{4} \))(\( 1 - 68 T^{2} + 1110 T^{4} - 468452 T^{6} + 47458321 T^{8} \))
$89$ (\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 197 T^{2} + 890 T^{3} + 7921 T^{4} )^{2} \))
$97$ (\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 + 136 T^{2} + 17298 T^{4} + 1279624 T^{6} + 88529281 T^{8} \))
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