Properties

Label 105.2.d
Level 105
Weight 2
Character orbit d
Rep. character \(\chi_{105}(64,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 2
Sturm bound 32
Trace bound 1

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 20 8 12
Cusp forms 12 8 4
Eisenstein series 8 0 8

Trace form

\( 8q - 8q^{4} + 4q^{5} - 4q^{6} - 8q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 4q^{5} - 4q^{6} - 8q^{9} - 8q^{10} + 4q^{15} + 24q^{16} - 28q^{20} + 4q^{21} + 12q^{24} - 8q^{25} + 24q^{26} - 12q^{30} - 16q^{31} + 32q^{34} + 4q^{35} + 8q^{36} - 8q^{39} + 16q^{40} + 8q^{41} - 32q^{44} - 4q^{45} - 16q^{46} - 8q^{49} - 8q^{50} + 8q^{51} + 4q^{54} - 8q^{55} - 24q^{56} - 16q^{59} - 4q^{60} - 16q^{61} - 40q^{64} + 24q^{65} + 8q^{66} + 8q^{69} + 8q^{70} + 32q^{71} + 80q^{74} + 16q^{75} + 16q^{76} - 32q^{79} + 44q^{80} + 8q^{81} - 12q^{84} + 16q^{85} - 40q^{89} + 8q^{90} + 16q^{91} + 32q^{94} + 16q^{95} - 68q^{96} + O(q^{100}) \)

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.d.a \(2\) \(0.838\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}+(1-2i)q^{5}-q^{6}+\cdots\)
105.2.d.b \(6\) \(0.838\) 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 3 T^{2} + 4 T^{4} \))(\( 1 - T^{2} - T^{4} - 3 T^{6} - 4 T^{8} - 16 T^{10} + 64 T^{12} \))
$3$ (\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{3} \))
$5$ (\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 3 T^{2} - 12 T^{3} + 15 T^{4} - 50 T^{5} + 125 T^{6} \))
$7$ (\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{3} \))
$11$ (\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 2 T + 11 T^{2} )^{6} \))
$13$ (\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 34 T^{2} + 359 T^{4} - 2172 T^{6} + 60671 T^{8} - 971074 T^{10} + 4826809 T^{12} \))
$17$ (\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 70 T^{2} + 2415 T^{4} - 51220 T^{6} + 697935 T^{8} - 5846470 T^{10} + 24137569 T^{12} \))
$19$ (\( ( 1 - 6 T + 19 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} + 188 T^{3} + 1007 T^{4} + 2166 T^{5} + 6859 T^{6} )^{2} \))
$23$ (\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 106 T^{2} + 5183 T^{4} - 150348 T^{6} + 2741807 T^{8} - 29663146 T^{10} + 148035889 T^{12} \))
$29$ (\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 35 T^{2} + 76 T^{3} + 1015 T^{4} + 1682 T^{5} + 24389 T^{6} )^{2} \))
$31$ (\( ( 1 + 10 T + 31 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} + 60 T^{3} + 1271 T^{4} - 1922 T^{5} + 29791 T^{6} )^{2} \))
$37$ (\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 46 T^{2} + 1399 T^{4} - 74788 T^{6} + 1915231 T^{8} - 86211406 T^{10} + 2565726409 T^{12} \))
$41$ (\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 63 T^{2} + 36 T^{3} + 2583 T^{4} - 3362 T^{5} + 68921 T^{6} )^{2} \))
$43$ (\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 46 T^{2} + 2839 T^{4} + 118948 T^{6} + 5249311 T^{8} + 157264846 T^{10} + 6321363049 T^{12} \))
$47$ (\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 154 T^{2} + 12143 T^{4} - 652332 T^{6} + 26823887 T^{8} - 751470874 T^{10} + 10779215329 T^{12} \))
$53$ (\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 146 T^{2} + 14103 T^{4} - 884828 T^{6} + 39615327 T^{8} - 1152010226 T^{10} + 22164361129 T^{12} \))
$59$ (\( ( 1 - 8 T + 59 T^{2} )^{2} \))(\( ( 1 + 16 T + 113 T^{2} + 608 T^{3} + 6667 T^{4} + 55696 T^{5} + 205379 T^{6} )^{2} \))
$61$ (\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 6 T + 131 T^{2} + 484 T^{3} + 7991 T^{4} + 22326 T^{5} + 226981 T^{6} )^{2} \))
$67$ (\( 1 + 122 T^{2} + 4489 T^{4} \))(\( 1 - 274 T^{2} + 36103 T^{4} - 2962972 T^{6} + 162066367 T^{8} - 5521407154 T^{10} + 90458382169 T^{12} \))
$71$ (\( ( 1 - 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 2 T + 71 T^{2} )^{6} \))
$73$ (\( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \))(\( 1 - 298 T^{2} + 43775 T^{4} - 3982284 T^{6} + 233276975 T^{8} - 8462675818 T^{10} + 151334226289 T^{12} \))
$79$ (\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 221 T^{2} + 1576 T^{3} + 17459 T^{4} + 74892 T^{5} + 493039 T^{6} )^{2} \))
$83$ (\( 1 - 102 T^{2} + 6889 T^{4} \))(\( 1 - 306 T^{2} + 47783 T^{4} - 4793948 T^{6} + 329177087 T^{8} - 14522246226 T^{10} + 326940373369 T^{12} \))
$89$ (\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 319 T^{2} + 2532 T^{3} + 28391 T^{4} + 110894 T^{5} + 704969 T^{6} )^{2} \))
$97$ (\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 26 T^{2} + 8719 T^{4} + 446932 T^{6} + 82037071 T^{8} - 2301761306 T^{10} + 832972004929 T^{12} \))
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