Properties

Label 224.3.v
Level 224
Weight 3
Character orbit v
Rep. character \(\chi_{224}(13,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 248
Newform subspaces 2
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(224, [\chi])\).

Total New Old
Modular forms 264 264 0
Cusp forms 248 248 0
Eisenstein series 16 16 0

Trace form

\( 248q - 8q^{2} - 8q^{4} - 4q^{7} - 8q^{8} - 8q^{9} + O(q^{10}) \) \( 248q - 8q^{2} - 8q^{4} - 4q^{7} - 8q^{8} - 8q^{9} - 8q^{11} + 12q^{14} + 12q^{16} - 68q^{18} - 4q^{21} - 44q^{22} + 56q^{23} - 8q^{25} + 56q^{28} - 8q^{29} - 16q^{30} - 8q^{32} + 92q^{35} + 192q^{36} - 8q^{37} - 8q^{39} - 424q^{42} - 104q^{43} + 308q^{44} - 8q^{46} - 320q^{50} - 80q^{51} - 168q^{53} + 356q^{56} - 8q^{57} - 712q^{58} + 264q^{60} - 8q^{63} - 272q^{64} - 16q^{65} - 168q^{67} + 320q^{70} + 504q^{71} - 8q^{72} + 124q^{74} - 4q^{77} + 560q^{78} - 1000q^{84} - 208q^{85} - 8q^{86} - 800q^{88} + 188q^{91} + 852q^{92} + 64q^{93} - 16q^{95} - 376q^{98} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
224.3.v.a \(8\) \(6.104\) 8.0.157351936.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{6}-\beta _{7})q^{2}+(-\beta _{3}+3\beta _{5})q^{4}+\cdots\)
224.3.v.b \(240\) \(6.104\) None \(-8\) \(0\) \(0\) \(-4\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 31 T^{4} + 256 T^{8} \))
$3$ (\( ( 1 + 6561 T^{8} )^{2} \))
$5$ (\( ( 1 + 390625 T^{8} )^{2} \))
$7$ (\( ( 1 + 2401 T^{4} )^{2} \))
$11$ (\( ( 1 - 206 T^{2} + 14641 T^{4} )^{2}( 1 + 13154 T^{4} + 214358881 T^{8} ) \))
$13$ (\( ( 1 + 815730721 T^{8} )^{2} \))
$17$ (\( ( 1 + 289 T^{2} )^{8} \))
$19$ (\( ( 1 + 16983563041 T^{8} )^{2} \))
$23$ (\( ( 1 + 18 T + 529 T^{2} )^{4}( 1 - 734 T^{2} + 279841 T^{4} )^{2} \))
$29$ (\( ( 1 + 1234 T^{2} + 707281 T^{4} )^{2}( 1 + 108194 T^{4} + 500246412961 T^{8} ) \))
$31$ (\( ( 1 - 31 T )^{8}( 1 + 31 T )^{8} \))
$37$ (\( ( 1 - 1294 T^{2} + 1874161 T^{4} )^{2}( 1 - 2073886 T^{4} + 3512479453921 T^{8} ) \))
$41$ (\( ( 1 + 2825761 T^{4} )^{4} \))
$43$ (\( ( 1 + 58 T + 1849 T^{2} )^{4}( 1 - 6726046 T^{4} + 11688200277601 T^{8} ) \))
$47$ (\( ( 1 + 2209 T^{2} )^{8} \))
$53$ (\( ( 1 - 6 T + 2809 T^{2} )^{4}( 1 + 15377762 T^{4} + 62259690411361 T^{8} ) \))
$59$ (\( ( 1 + 146830437604321 T^{8} )^{2} \))
$61$ (\( ( 1 + 191707312997281 T^{8} )^{2} \))
$67$ (\( ( 1 + 118 T + 4489 T^{2} )^{4}( 1 - 15839326 T^{4} + 406067677556641 T^{8} ) \))
$71$ (\( ( 1 - 42331966 T^{4} + 645753531245761 T^{8} )^{2} \))
$73$ (\( ( 1 + 28398241 T^{4} )^{4} \))
$79$ (\( ( 1 - 64606846 T^{4} + 1517108809906561 T^{8} )^{2} \))
$83$ (\( ( 1 + 2252292232139041 T^{8} )^{2} \))
$89$ (\( ( 1 + 62742241 T^{4} )^{4} \))
$97$ (\( ( 1 - 97 T )^{8}( 1 + 97 T )^{8} \))
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