Properties

Label 14.5.b
Level 14
Weight 5
Character orbit b
Rep. character \(\chi_{14}(13,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 14.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(14, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

\( 4q + 32q^{4} - 76q^{7} - 252q^{9} + O(q^{10}) \) \( 4q + 32q^{4} - 76q^{7} - 252q^{9} + 360q^{11} - 288q^{14} + 384q^{15} + 256q^{16} + 192q^{18} + 768q^{21} - 1152q^{22} - 792q^{23} - 2300q^{25} - 608q^{28} + 1224q^{29} + 4416q^{30} + 4032q^{35} - 2016q^{36} - 3896q^{37} - 768q^{39} - 4800q^{42} + 3688q^{43} + 2880q^{44} + 3072q^{46} - 1532q^{49} - 7488q^{50} - 11136q^{51} + 5832q^{53} - 2304q^{56} + 12864q^{57} + 7296q^{58} + 3072q^{60} + 3060q^{63} + 2048q^{64} - 4032q^{65} - 1048q^{67} - 1344q^{70} - 21528q^{71} + 1536q^{72} - 3456q^{74} + 3528q^{77} + 4800q^{78} + 12776q^{79} - 29628q^{81} + 6144q^{84} + 16512q^{85} - 11520q^{86} - 9216q^{88} + 5568q^{91} - 6336q^{92} + 38016q^{93} + 36864q^{95} + 21888q^{98} - 29592q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
14.5.b.a \(4\) \(1.447\) 4.0.1308672.3 None \(0\) \(0\) \(0\) \(-76\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - 8 T^{2} )^{2} \)
$3$ \( 1 - 36 T^{2} + 13158 T^{4} - 236196 T^{6} + 43046721 T^{8} \)
$5$ \( 1 - 100 T^{2} + 345702 T^{4} - 39062500 T^{6} + 152587890625 T^{8} \)
$7$ \( 1 + 76 T + 3654 T^{2} + 182476 T^{3} + 5764801 T^{4} \)
$11$ \( ( 1 - 180 T + 27014 T^{2} - 2635380 T^{3} + 214358881 T^{4} )^{2} \)
$13$ \( 1 - 111460 T^{2} + 4736358630 T^{4} - 90921346162660 T^{6} + 665416609183179841 T^{8} \)
$17$ \( 1 - 217348 T^{2} + 25123879686 T^{4} - 1516166928286468 T^{6} + 48661191875666868481 T^{8} \)
$19$ \( 1 - 150436 T^{2} + 9183572838 T^{4} - 2554939289635876 T^{6} + \)\(28\!\cdots\!81\)\( T^{8} \)
$23$ \( ( 1 + 396 T + 525158 T^{2} + 110817036 T^{3} + 78310985281 T^{4} )^{2} \)
$29$ \( ( 1 - 612 T + 1092326 T^{2} - 432855972 T^{3} + 500246412961 T^{4} )^{2} \)
$31$ \( 1 - 1703428 T^{2} + 1577900136966 T^{4} - 1452838474126047748 T^{6} + \)\(72\!\cdots\!81\)\( T^{8} \)
$37$ \( ( 1 + 1948 T + 4603686 T^{2} + 3650865628 T^{3} + 3512479453921 T^{4} )^{2} \)
$41$ \( 1 - 7851268 T^{2} + 31379741059206 T^{4} - 62691787933790375428 T^{6} + \)\(63\!\cdots\!41\)\( T^{8} \)
$43$ \( ( 1 - 1844 T + 6650886 T^{2} - 6304269044 T^{3} + 11688200277601 T^{4} )^{2} \)
$47$ \( 1 - 10858756 T^{2} + 58650967963398 T^{4} - \)\(25\!\cdots\!16\)\( T^{6} + \)\(56\!\cdots\!21\)\( T^{8} \)
$53$ \( ( 1 - 2916 T + 9386534 T^{2} - 23008642596 T^{3} + 62259690411361 T^{4} )^{2} \)
$59$ \( 1 - 42750244 T^{2} + 750538168343526 T^{4} - \)\(62\!\cdots\!24\)\( T^{6} + \)\(21\!\cdots\!41\)\( T^{8} \)
$61$ \( 1 - 28277476 T^{2} + 401277478909158 T^{4} - \)\(54\!\cdots\!56\)\( T^{6} + \)\(36\!\cdots\!61\)\( T^{8} \)
$67$ \( ( 1 + 524 T + 39707334 T^{2} + 10559187404 T^{3} + 406067677556641 T^{4} )^{2} \)
$71$ \( ( 1 + 10764 T + 70144454 T^{2} + 273531334284 T^{3} + 645753531245761 T^{4} )^{2} \)
$73$ \( 1 - 62983684 T^{2} + 1969418053172358 T^{4} - \)\(50\!\cdots\!04\)\( T^{6} + \)\(65\!\cdots\!61\)\( T^{8} \)
$79$ \( ( 1 - 6388 T + 73521798 T^{2} - 248813117428 T^{3} + 1517108809906561 T^{4} )^{2} \)
$83$ \( 1 - 129024292 T^{2} + 7865129580692070 T^{4} - \)\(29\!\cdots\!72\)\( T^{6} + \)\(50\!\cdots\!81\)\( T^{8} \)
$89$ \( 1 - 228854020 T^{2} + 20924407354852230 T^{4} - \)\(90\!\cdots\!20\)\( T^{6} + \)\(15\!\cdots\!61\)\( T^{8} \)
$97$ \( 1 - 150468100 T^{2} + 16842128301249030 T^{4} - \)\(11\!\cdots\!00\)\( T^{6} + \)\(61\!\cdots\!21\)\( T^{8} \)
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