Properties

Label 105.2.b
Level 105
Weight 2
Character orbit b
Rep. character \(\chi_{105}(41,\cdot)\)
Character field \(\Q\)
Dimension 12
Newform subspaces 4
Sturm bound 32
Trace bound 5

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Defining parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(17\)

Dimensions

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

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

Trace form

\( 12q - 16q^{4} - 8q^{7} - 2q^{9} + O(q^{10}) \) \( 12q - 16q^{4} - 8q^{7} - 2q^{9} + 2q^{15} + 8q^{16} - 4q^{18} + 6q^{21} + 8q^{22} + 12q^{25} + 16q^{28} + 4q^{30} - 36q^{36} - 16q^{37} + 30q^{39} + 36q^{42} - 40q^{43} - 16q^{46} + 12q^{49} - 30q^{51} - 12q^{57} + 8q^{58} - 36q^{60} - 44q^{63} - 8q^{64} + 24q^{67} + 64q^{72} + 84q^{78} + 36q^{79} + 22q^{81} - 36q^{84} - 12q^{85} + 16q^{88} - 12q^{91} + 12q^{93} + 26q^{99} + O(q^{100}) \)

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.b.a \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(4\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-q^{5}-3q^{6}+\cdots\)
105.2.b.b \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(4\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+q^{5}+3q^{6}+\cdots\)
105.2.b.c \(4\) \(0.838\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(-4\) \(-8\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)
105.2.b.d \(4\) \(0.838\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(4\) \(-8\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T^{2} + 4 T^{4} \))(\( 1 - T^{2} + 4 T^{4} \))(\( 1 - T^{2} - 4 T^{6} + 16 T^{8} \))(\( 1 - T^{2} - 4 T^{6} + 16 T^{8} \))
$3$ (\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))
$5$ (\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))
$7$ (\( 1 - 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))
$11$ (\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 - 37 T^{2} + 576 T^{4} - 4477 T^{6} + 14641 T^{8} \))(\( 1 - 37 T^{2} + 576 T^{4} - 4477 T^{6} + 14641 T^{8} \))
$13$ (\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - T^{2} + 264 T^{4} - 169 T^{6} + 28561 T^{8} \))(\( 1 - T^{2} + 264 T^{4} - 169 T^{6} + 28561 T^{8} \))
$17$ (\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 3 T + 28 T^{2} + 51 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 3 T + 28 T^{2} - 51 T^{3} + 289 T^{4} )^{2} \))
$19$ (\( ( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2} \))
$23$ (\( 1 - 34 T^{2} + 529 T^{4} \))(\( 1 - 34 T^{2} + 529 T^{4} \))(\( 1 - 16 T^{2} - 66 T^{4} - 8464 T^{6} + 279841 T^{8} \))(\( 1 - 16 T^{2} - 66 T^{4} - 8464 T^{6} + 279841 T^{8} \))
$29$ (\( 1 - 10 T^{2} + 841 T^{4} \))(\( 1 - 10 T^{2} + 841 T^{4} \))(\( 1 - 97 T^{2} + 3960 T^{4} - 81577 T^{6} + 707281 T^{8} \))(\( 1 - 97 T^{2} + 3960 T^{4} - 81577 T^{6} + 707281 T^{8} \))
$31$ (\( 1 - 50 T^{2} + 961 T^{4} \))(\( 1 - 50 T^{2} + 961 T^{4} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 42 T^{2} + 74 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 2 T + 42 T^{2} + 74 T^{3} + 1369 T^{4} )^{2} \))
$41$ (\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{4} \))(\( ( 1 + 6 T + 41 T^{2} )^{4} \))
$43$ (\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 2 T + 54 T^{2} + 86 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 2 T + 54 T^{2} + 86 T^{3} + 1849 T^{4} )^{2} \))
$47$ (\( ( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 - 12 T + 47 T^{2} )^{2} \))(\( ( 1 - 9 T + 106 T^{2} - 423 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 9 T + 106 T^{2} + 423 T^{3} + 2209 T^{4} )^{2} \))
$53$ (\( ( 1 - 53 T^{2} )^{2} \))(\( ( 1 - 53 T^{2} )^{2} \))(\( 1 - 136 T^{2} + 9054 T^{4} - 382024 T^{6} + 7890481 T^{8} \))(\( 1 - 136 T^{2} + 9054 T^{4} - 382024 T^{6} + 7890481 T^{8} \))
$59$ (\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 6 T + 94 T^{2} - 354 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 6 T + 94 T^{2} + 354 T^{3} + 3481 T^{4} )^{2} \))
$61$ (\( ( 1 - 14 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} ) \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} ) \))(\( ( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2} \))
$67$ (\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 2 T + 102 T^{2} + 134 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 2 T + 102 T^{2} + 134 T^{3} + 4489 T^{4} )^{2} \))
$71$ (\( 1 - 130 T^{2} + 5041 T^{4} \))(\( 1 - 130 T^{2} + 5041 T^{4} \))(\( 1 - 100 T^{2} + 4134 T^{4} - 504100 T^{6} + 25411681 T^{8} \))(\( 1 - 100 T^{2} + 4134 T^{4} - 504100 T^{6} + 25411681 T^{8} \))
$73$ (\( 1 - 98 T^{2} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))(\( ( 1 - 98 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 98 T^{2} + 5329 T^{4} )^{2} \))
$79$ (\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - T + 150 T^{2} - 79 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - T + 150 T^{2} - 79 T^{3} + 6241 T^{4} )^{2} \))
$83$ (\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 70 T^{2} - 996 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 12 T + 70 T^{2} + 996 T^{3} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 18 T + 226 T^{2} + 1602 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 18 T + 226 T^{2} - 1602 T^{3} + 7921 T^{4} )^{2} \))
$97$ (\( 1 - 146 T^{2} + 9409 T^{4} \))(\( 1 - 146 T^{2} + 9409 T^{4} \))(\( 1 - 265 T^{2} + 32736 T^{4} - 2493385 T^{6} + 88529281 T^{8} \))(\( 1 - 265 T^{2} + 32736 T^{4} - 2493385 T^{6} + 88529281 T^{8} \))
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