Properties

Label 105.2.g
Level 105
Weight 2
Character orbit g
Rep. character \(\chi_{105}(104,\cdot)\)
Character field \(\Q\)
Dimension 12
Newform subspaces 3
Sturm bound 32
Trace bound 3

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Defining parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\( 12q - 6q^{9} + O(q^{10}) \) \( 12q - 6q^{9} + 6q^{15} - 24q^{16} + 6q^{21} - 12q^{25} - 24q^{30} - 12q^{36} + 18q^{39} + 48q^{46} - 12q^{49} + 42q^{51} + 36q^{60} - 24q^{64} + 24q^{70} + 60q^{79} - 90q^{81} - 36q^{84} - 12q^{85} - 60q^{91} + 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.2.g.a \(4\) \(0.838\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(-4\) \(0\) \(4\) \(q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
105.2.g.b \(4\) \(0.838\) \(\Q(\sqrt{-5}, \sqrt{7})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-2q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
105.2.g.c \(4\) \(0.838\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(4\) \(0\) \(-4\) \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T^{2} + 4 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} )^{4} \))(\( ( 1 + T^{2} + 4 T^{4} )^{2} \))
$3$ (\( ( 1 + 2 T + 3 T^{2} )^{2} \))(\( 1 - T^{2} + 9 T^{4} \))(\( ( 1 - 2 T + 3 T^{2} )^{2} \))
$5$ (\( 1 - 2 T^{2} + 25 T^{4} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 25 T^{4} \))
$7$ (\( ( 1 - 2 T + 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))
$11$ (\( ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2}( 1 + 3 T + 11 T^{2} )^{2} \))(\( ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2} \))
$13$ (\( ( 1 + 4 T + 13 T^{2} )^{4} \))(\( ( 1 + 19 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{4} \))
$17$ (\( ( 1 - 26 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 29 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 289 T^{4} )^{2} \))
$19$ (\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 19 T^{2} )^{4} \))
$23$ (\( ( 1 + 34 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 23 T^{2} )^{4} \))(\( ( 1 + 34 T^{2} + 529 T^{4} )^{2} \))
$29$ (\( ( 1 - 26 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 9 T + 29 T^{2} )^{2}( 1 + 9 T + 29 T^{2} )^{2} \))(\( ( 1 - 26 T^{2} + 841 T^{4} )^{2} \))
$31$ (\( ( 1 + 34 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 31 T^{2} )^{4} \))(\( ( 1 + 34 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( ( 1 - 37 T^{2} )^{4} \))(\( ( 1 - 37 T^{2} )^{4} \))(\( ( 1 - 37 T^{2} )^{4} \))
$41$ (\( ( 1 + 70 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 41 T^{2} )^{4} \))(\( ( 1 + 70 T^{2} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 - 62 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 43 T^{2} )^{4} \))(\( ( 1 - 62 T^{2} + 1849 T^{4} )^{2} \))
$47$ (\( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 + 31 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \))
$53$ (\( ( 1 + 53 T^{2} )^{4} \))(\( ( 1 + 53 T^{2} )^{4} \))(\( ( 1 + 53 T^{2} )^{4} \))
$59$ (\( ( 1 + 70 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 59 T^{2} )^{4} \))(\( ( 1 + 70 T^{2} + 3481 T^{4} )^{2} \))
$61$ (\( ( 1 - 26 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 - 26 T^{2} + 3721 T^{4} )^{2} \))
$67$ (\( ( 1 - 110 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 67 T^{2} )^{4} \))(\( ( 1 - 110 T^{2} + 4489 T^{4} )^{2} \))
$71$ (\( ( 1 - 134 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2}( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 134 T^{2} + 5041 T^{4} )^{2} \))
$73$ (\( ( 1 - 8 T + 73 T^{2} )^{4} \))(\( ( 1 + 34 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 8 T + 73 T^{2} )^{4} \))
$79$ (\( ( 1 - 8 T + 79 T^{2} )^{4} \))(\( ( 1 + T + 79 T^{2} )^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{4} \))
$83$ (\( ( 1 - 18 T + 83 T^{2} )^{2}( 1 + 18 T + 83 T^{2} )^{2} \))(\( ( 1 - 86 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 18 T + 83 T^{2} )^{2}( 1 + 18 T + 83 T^{2} )^{2} \))
$89$ (\( ( 1 + 70 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 89 T^{2} )^{4} \))(\( ( 1 + 70 T^{2} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 - 8 T + 97 T^{2} )^{4} \))(\( ( 1 - 149 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 + 8 T + 97 T^{2} )^{4} \))
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