Properties

Label 70.2.c
Level 70
Weight 2
Character orbit c
Rep. character \(\chi_{70}(29,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) = \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 70.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(70, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4q - 4q^{4} + 4q^{5} - 12q^{9} + O(q^{10}) \) \( 4q - 4q^{4} + 4q^{5} - 12q^{9} + 4q^{10} - 4q^{14} + 12q^{15} + 4q^{16} - 16q^{19} - 4q^{20} - 8q^{26} - 8q^{29} + 12q^{30} + 16q^{31} + 8q^{34} + 4q^{35} + 12q^{36} + 24q^{39} - 4q^{40} - 24q^{41} - 12q^{45} + 8q^{46} - 4q^{49} - 4q^{50} - 24q^{55} + 4q^{56} + 16q^{59} - 12q^{60} + 24q^{61} - 4q^{64} - 4q^{65} - 48q^{66} + 48q^{69} - 4q^{70} - 24q^{71} + 8q^{74} + 16q^{76} - 8q^{79} + 4q^{80} - 36q^{81} - 8q^{85} - 16q^{86} + 40q^{89} - 12q^{90} - 8q^{91} + 16q^{94} - 4q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(70, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
70.2.c.a \(4\) \(0.559\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(70, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + T^{2} )^{2} \)
$3$ \( ( 1 + 9 T^{4} )^{2} \)
$5$ \( 1 - 4 T + 8 T^{2} - 20 T^{3} + 25 T^{4} \)
$7$ \( ( 1 + T^{2} )^{2} \)
$11$ \( ( 1 - 2 T^{2} + 121 T^{4} )^{2} \)
$13$ \( 1 - 32 T^{2} + 498 T^{4} - 5408 T^{6} + 28561 T^{8} \)
$17$ \( ( 1 - 8 T + 17 T^{2} )^{2}( 1 + 8 T + 17 T^{2} )^{2} \)
$19$ \( ( 1 + 8 T + 48 T^{2} + 152 T^{3} + 361 T^{4} )^{2} \)
$23$ \( 1 - 36 T^{2} + 998 T^{4} - 19044 T^{6} + 279841 T^{8} \)
$29$ \( ( 1 + 4 T + 38 T^{2} + 116 T^{3} + 841 T^{4} )^{2} \)
$31$ \( ( 1 - 8 T + 54 T^{2} - 248 T^{3} + 961 T^{4} )^{2} \)
$37$ \( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \)
$41$ \( ( 1 + 12 T + 94 T^{2} + 492 T^{3} + 1681 T^{4} )^{2} \)
$43$ \( 1 - 92 T^{2} + 4278 T^{4} - 170108 T^{6} + 3418801 T^{8} \)
$47$ \( 1 - 108 T^{2} + 5798 T^{4} - 238572 T^{6} + 4879681 T^{8} \)
$53$ \( 1 - 92 T^{2} + 4278 T^{4} - 258428 T^{6} + 7890481 T^{8} \)
$59$ \( ( 1 - 8 T + 128 T^{2} - 472 T^{3} + 3481 T^{4} )^{2} \)
$61$ \( ( 1 - 12 T + 152 T^{2} - 732 T^{3} + 3721 T^{4} )^{2} \)
$67$ \( ( 1 - 70 T^{2} + 4489 T^{4} )^{2} \)
$71$ \( ( 1 + 12 T + 154 T^{2} + 852 T^{3} + 5041 T^{4} )^{2} \)
$73$ \( 1 - 236 T^{2} + 24198 T^{4} - 1257644 T^{6} + 28398241 T^{8} \)
$79$ \( ( 1 + 4 T + 138 T^{2} + 316 T^{3} + 6241 T^{4} )^{2} \)
$83$ \( ( 1 - 160 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( ( 1 - 10 T + 89 T^{2} )^{4} \)
$97$ \( 1 - 124 T^{2} + 8838 T^{4} - 1166716 T^{6} + 88529281 T^{8} \)
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