Properties

Label 15.5.d
Level 15
Weight 5
Character orbit d
Rep. character \(\chi_{15}(14,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 3
Sturm bound 10
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 15.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(10\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(15, [\chi])\).

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

Trace form

\( 6q + 42q^{4} - 66q^{6} + 18q^{9} + O(q^{10}) \) \( 6q + 42q^{4} - 66q^{6} + 18q^{9} - 270q^{10} + 570q^{15} + 114q^{16} + 756q^{19} + 468q^{21} - 3462q^{24} - 930q^{25} + 2340q^{30} - 3708q^{31} + 8868q^{34} + 6210q^{36} - 7488q^{39} - 7710q^{40} + 7020q^{45} - 6612q^{46} + 13470q^{49} - 1596q^{51} - 19386q^{54} - 9360q^{55} + 14130q^{60} + 9252q^{61} + 10530q^{64} + 9360q^{66} - 6096q^{69} - 4680q^{70} + 9360q^{75} - 23100q^{76} - 5724q^{79} - 2754q^{81} - 2808q^{84} - 12060q^{85} - 31230q^{90} + 14976q^{91} + 28188q^{94} + 9522q^{96} + 28080q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.5.d.a \(1\) \(1.551\) \(\Q\) \(\Q(\sqrt{-15}) \) \(-7\) \(9\) \(25\) \(0\) \(q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.b \(1\) \(1.551\) \(\Q\) \(\Q(\sqrt{-15}) \) \(7\) \(-9\) \(-25\) \(0\) \(q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.c \(4\) \(1.551\) \(\Q(\sqrt{10}, \sqrt{-26})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 7 T + 16 T^{2} \))(\( 1 - 7 T + 16 T^{2} \))(\( ( 1 + 22 T^{2} + 256 T^{4} )^{2} \))
$3$ (\( 1 - 9 T \))(\( 1 + 9 T \))(\( 1 + 72 T^{2} + 6561 T^{4} \))
$5$ (\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 + 1090 T^{2} + 390625 T^{4} \))
$7$ (\( ( 1 - 49 T )( 1 + 49 T ) \))(\( ( 1 - 49 T )( 1 + 49 T ) \))(\( ( 1 - 4568 T^{2} + 5764801 T^{4} )^{2} \))
$11$ (\( ( 1 - 121 T )( 1 + 121 T ) \))(\( ( 1 - 121 T )( 1 + 121 T ) \))(\( ( 1 - 19922 T^{2} + 214358881 T^{4} )^{2} \))
$13$ (\( ( 1 - 169 T )( 1 + 169 T ) \))(\( ( 1 - 169 T )( 1 + 169 T ) \))(\( ( 1 + 2782 T^{2} + 815730721 T^{4} )^{2} \))
$17$ (\( 1 + 382 T + 83521 T^{2} \))(\( 1 - 382 T + 83521 T^{2} \))(\( ( 1 + 89602 T^{2} + 6975757441 T^{4} )^{2} \))
$19$ (\( 1 + 238 T + 130321 T^{2} \))(\( 1 + 238 T + 130321 T^{2} \))(\( ( 1 - 308 T + 130321 T^{2} )^{4} \))
$23$ (\( 1 - 98 T + 279841 T^{2} \))(\( 1 + 98 T + 279841 T^{2} \))(\( ( 1 + 388072 T^{2} + 78310985281 T^{4} )^{2} \))
$29$ (\( ( 1 - 841 T )( 1 + 841 T ) \))(\( ( 1 - 841 T )( 1 + 841 T ) \))(\( ( 1 - 1377122 T^{2} + 500246412961 T^{4} )^{2} \))
$31$ (\( 1 + 1918 T + 923521 T^{2} \))(\( 1 + 1918 T + 923521 T^{2} \))(\( ( 1 - 32 T + 923521 T^{2} )^{4} \))
$37$ (\( ( 1 - 1369 T )( 1 + 1369 T ) \))(\( ( 1 - 1369 T )( 1 + 1369 T ) \))(\( ( 1 - 2097218 T^{2} + 3512479453921 T^{4} )^{2} \))
$41$ (\( ( 1 - 1681 T )( 1 + 1681 T ) \))(\( ( 1 - 1681 T )( 1 + 1681 T ) \))(\( ( 1 - 1324862 T^{2} + 7984925229121 T^{4} )^{2} \))
$43$ (\( ( 1 - 1849 T )( 1 + 1849 T ) \))(\( ( 1 - 1849 T )( 1 + 1849 T ) \))(\( ( 1 - 154328 T^{2} + 11688200277601 T^{4} )^{2} \))
$47$ (\( 1 + 4222 T + 4879681 T^{2} \))(\( 1 - 4222 T + 4879681 T^{2} \))(\( ( 1 + 3784072 T^{2} + 23811286661761 T^{4} )^{2} \))
$53$ (\( 1 - 1778 T + 7890481 T^{2} \))(\( 1 + 1778 T + 7890481 T^{2} \))(\( ( 1 + 13773922 T^{2} + 62259690411361 T^{4} )^{2} \))
$59$ (\( ( 1 - 3481 T )( 1 + 3481 T ) \))(\( ( 1 - 3481 T )( 1 + 3481 T ) \))(\( ( 1 - 8500562 T^{2} + 146830437604321 T^{4} )^{2} \))
$61$ (\( 1 - 6482 T + 13845841 T^{2} \))(\( 1 - 6482 T + 13845841 T^{2} \))(\( ( 1 + 928 T + 13845841 T^{2} )^{4} \))
$67$ (\( ( 1 - 4489 T )( 1 + 4489 T ) \))(\( ( 1 - 4489 T )( 1 + 4489 T ) \))(\( ( 1 - 33618968 T^{2} + 406067677556641 T^{4} )^{2} \))
$71$ (\( ( 1 - 5041 T )( 1 + 5041 T ) \))(\( ( 1 - 5041 T )( 1 + 5041 T ) \))(\( ( 1 - 29257922 T^{2} + 645753531245761 T^{4} )^{2} \))
$73$ (\( ( 1 - 5329 T )( 1 + 5329 T ) \))(\( ( 1 - 5329 T )( 1 + 5329 T ) \))(\( ( 1 - 38971298 T^{2} + 806460091894081 T^{4} )^{2} \))
$79$ (\( 1 + 2878 T + 38950081 T^{2} \))(\( 1 + 2878 T + 38950081 T^{2} \))(\( ( 1 - 8 T + 38950081 T^{2} )^{4} \))
$83$ (\( 1 - 9938 T + 47458321 T^{2} \))(\( 1 + 9938 T + 47458321 T^{2} \))(\( ( 1 + 75232552 T^{2} + 2252292232139041 T^{4} )^{2} \))
$89$ (\( ( 1 - 7921 T )( 1 + 7921 T ) \))(\( ( 1 - 7921 T )( 1 + 7921 T ) \))(\( ( 1 - 39222722 T^{2} + 3936588805702081 T^{4} )^{2} \))
$97$ (\( ( 1 - 9409 T )( 1 + 9409 T ) \))(\( ( 1 - 9409 T )( 1 + 9409 T ) \))(\( ( 1 - 170764898 T^{2} + 7837433594376961 T^{4} )^{2} \))
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