Properties

Label 18.10.a
Level 18
Weight 10
Character orbit a
Rep. character \(\chi_{18}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 4
Sturm bound 30
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 18.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(30\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(18))\).

Total New Old
Modular forms 31 4 27
Cusp forms 23 4 19
Eisenstein series 8 0 8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(2\)

Trace form

\( 4q + 1024q^{4} - 3564q^{5} + 7208q^{7} + O(q^{10}) \) \( 4q + 1024q^{4} - 3564q^{5} + 7208q^{7} - 16896q^{10} + 26568q^{11} - 72352q^{13} - 41472q^{14} + 262144q^{16} + 349596q^{17} - 837352q^{19} - 912384q^{20} + 1528320q^{22} + 908496q^{23} + 496948q^{25} - 3566592q^{26} + 1845248q^{28} + 6197796q^{29} - 16588648q^{31} + 12340224q^{34} + 10375776q^{35} + 7630136q^{37} - 19367424q^{38} - 4325376q^{40} - 27730836q^{41} + 35353736q^{43} + 6801408q^{44} - 19716096q^{46} + 31547232q^{47} - 79456380q^{49} + 104011776q^{50} - 18522112q^{52} - 73867788q^{53} + 100438992q^{55} - 10616832q^{56} - 180045312q^{58} - 145822680q^{59} + 464275736q^{61} + 23763456q^{62} + 67108864q^{64} - 34202088q^{65} - 666162424q^{67} + 89496576q^{68} + 211418112q^{70} + 306248688q^{71} - 64987264q^{73} - 115623936q^{74} - 214362112q^{76} + 51378624q^{77} + 289293560q^{79} - 233570304q^{80} + 410661888q^{82} + 439073784q^{83} - 137951208q^{85} - 838937088q^{86} + 391249920q^{88} - 658833588q^{89} - 1214045552q^{91} + 232574976q^{92} + 787934208q^{94} + 2136975696q^{95} + 151355744q^{97} + 186458112q^{98} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
18.10.a.a \(1\) \(9.271\) \(\Q\) None \(-16\) \(0\) \(-870\) \(-952\) \(+\) \(-\) \(q-2^{4}q^{2}+2^{8}q^{4}-870q^{5}-952q^{7}+\cdots\)
18.10.a.b \(1\) \(9.271\) \(\Q\) None \(-16\) \(0\) \(-384\) \(5852\) \(+\) \(+\) \(q-2^{4}q^{2}+2^{8}q^{4}-384q^{5}+5852q^{7}+\cdots\)
18.10.a.c \(1\) \(9.271\) \(\Q\) None \(16\) \(0\) \(-2694\) \(-3544\) \(-\) \(-\) \(q+2^{4}q^{2}+2^{8}q^{4}-2694q^{5}-3544q^{7}+\cdots\)
18.10.a.d \(1\) \(9.271\) \(\Q\) None \(16\) \(0\) \(384\) \(5852\) \(-\) \(+\) \(q+2^{4}q^{2}+2^{8}q^{4}+384q^{5}+5852q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 16 T \))(\( 1 + 16 T \))(\( 1 - 16 T \))(\( 1 - 16 T \))
$3$ 1
$5$ (\( 1 + 870 T + 1953125 T^{2} \))(\( 1 + 384 T + 1953125 T^{2} \))(\( 1 + 2694 T + 1953125 T^{2} \))(\( 1 - 384 T + 1953125 T^{2} \))
$7$ (\( 1 + 952 T + 40353607 T^{2} \))(\( 1 - 5852 T + 40353607 T^{2} \))(\( 1 + 3544 T + 40353607 T^{2} \))(\( 1 - 5852 T + 40353607 T^{2} \))
$11$ (\( 1 - 56148 T + 2357947691 T^{2} \))(\( 1 + 90624 T + 2357947691 T^{2} \))(\( 1 + 29580 T + 2357947691 T^{2} \))(\( 1 - 90624 T + 2357947691 T^{2} \))
$13$ (\( 1 - 178094 T + 10604499373 T^{2} \))(\( 1 + 102814 T + 10604499373 T^{2} \))(\( 1 + 44818 T + 10604499373 T^{2} \))(\( 1 + 102814 T + 10604499373 T^{2} \))
$17$ (\( 1 - 247662 T + 118587876497 T^{2} \))(\( 1 + 458496 T + 118587876497 T^{2} \))(\( 1 - 101934 T + 118587876497 T^{2} \))(\( 1 - 458496 T + 118587876497 T^{2} \))
$19$ (\( 1 - 315380 T + 322687697779 T^{2} \))(\( 1 + 128824 T + 322687697779 T^{2} \))(\( 1 + 895084 T + 322687697779 T^{2} \))(\( 1 + 128824 T + 322687697779 T^{2} \))
$23$ (\( 1 + 204504 T + 1801152661463 T^{2} \))(\( 1 - 1274880 T + 1801152661463 T^{2} \))(\( 1 - 1113000 T + 1801152661463 T^{2} \))(\( 1 + 1274880 T + 1801152661463 T^{2} \))
$29$ (\( 1 - 3840450 T + 14507145975869 T^{2} \))(\( 1 - 4884864 T + 14507145975869 T^{2} \))(\( 1 - 2357346 T + 14507145975869 T^{2} \))(\( 1 + 4884864 T + 14507145975869 T^{2} \))
$31$ (\( 1 + 1309408 T + 26439622160671 T^{2} \))(\( 1 + 7727524 T + 26439622160671 T^{2} \))(\( 1 - 175808 T + 26439622160671 T^{2} \))(\( 1 + 7727524 T + 26439622160671 T^{2} \))
$37$ (\( 1 - 4307078 T + 129961739795077 T^{2} \))(\( 1 - 3121238 T + 129961739795077 T^{2} \))(\( 1 + 2919418 T + 129961739795077 T^{2} \))(\( 1 - 3121238 T + 129961739795077 T^{2} \))
$41$ (\( 1 + 1512042 T + 327381934393961 T^{2} \))(\( 1 + 25186560 T + 327381934393961 T^{2} \))(\( 1 + 26218794 T + 327381934393961 T^{2} \))(\( 1 - 25186560 T + 327381934393961 T^{2} \))
$43$ (\( 1 - 33670604 T + 502592611936843 T^{2} \))(\( 1 - 10223048 T + 502592611936843 T^{2} \))(\( 1 + 18762964 T + 502592611936843 T^{2} \))(\( 1 - 10223048 T + 502592611936843 T^{2} \))
$47$ (\( 1 - 10581072 T + 1119130473102767 T^{2} \))(\( 1 + 19430400 T + 1119130473102767 T^{2} \))(\( 1 - 20966160 T + 1119130473102767 T^{2} \))(\( 1 - 19430400 T + 1119130473102767 T^{2} \))
$53$ (\( 1 + 16616214 T + 3299763591802133 T^{2} \))(\( 1 - 59935104 T + 3299763591802133 T^{2} \))(\( 1 + 57251574 T + 3299763591802133 T^{2} \))(\( 1 + 59935104 T + 3299763591802133 T^{2} \))
$59$ (\( 1 + 112235100 T + 8662995818654939 T^{2} \))(\( 1 - 75334656 T + 8662995818654939 T^{2} \))(\( 1 + 33587580 T + 8662995818654939 T^{2} \))(\( 1 + 75334656 T + 8662995818654939 T^{2} \))
$61$ (\( 1 + 33197218 T + 11694146092834141 T^{2} \))(\( 1 - 207606062 T + 11694146092834141 T^{2} \))(\( 1 - 82260830 T + 11694146092834141 T^{2} \))(\( 1 - 207606062 T + 11694146092834141 T^{2} \))
$67$ (\( 1 + 121372252 T + 27206534396294947 T^{2} \))(\( 1 + 178167184 T + 27206534396294947 T^{2} \))(\( 1 + 188455804 T + 27206534396294947 T^{2} \))(\( 1 + 178167184 T + 27206534396294947 T^{2} \))
$71$ (\( 1 - 387172728 T + 45848500718449031 T^{2} \))(\( 1 + 4902912 T + 45848500718449031 T^{2} \))(\( 1 + 80924040 T + 45848500718449031 T^{2} \))(\( 1 - 4902912 T + 45848500718449031 T^{2} \))
$73$ (\( 1 - 255240074 T + 58871586708267913 T^{2} \))(\( 1 + 42043210 T + 58871586708267913 T^{2} \))(\( 1 + 236140918 T + 58871586708267913 T^{2} \))(\( 1 + 42043210 T + 58871586708267913 T^{2} \))
$79$ (\( 1 - 492101840 T + 119851595982618319 T^{2} \))(\( 1 + 364859044 T + 119851595982618319 T^{2} \))(\( 1 - 526909808 T + 119851595982618319 T^{2} \))(\( 1 + 364859044 T + 119851595982618319 T^{2} \))
$83$ (\( 1 - 457420236 T + 186940255267540403 T^{2} \))(\( 1 + 317941248 T + 186940255267540403 T^{2} \))(\( 1 + 18346452 T + 186940255267540403 T^{2} \))(\( 1 - 317941248 T + 186940255267540403 T^{2} \))
$89$ (\( 1 - 31809510 T + 350356403707485209 T^{2} \))(\( 1 - 788009472 T + 350356403707485209 T^{2} \))(\( 1 + 690643098 T + 350356403707485209 T^{2} \))(\( 1 + 788009472 T + 350356403707485209 T^{2} \))
$97$ (\( 1 + 673532062 T + 760231058654565217 T^{2} \))(\( 1 - 631569422 T + 760231058654565217 T^{2} \))(\( 1 + 438251038 T + 760231058654565217 T^{2} \))(\( 1 - 631569422 T + 760231058654565217 T^{2} \))
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