Properties

Label 18.6.a
Level 18
Weight 6
Character orbit a
Rep. character \(\chi_{18}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 3
Sturm bound 18
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 18.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(18\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(18))\).

Total New Old
Modular forms 19 3 16
Cusp forms 11 3 8
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3q - 4q^{2} + 48q^{4} + 66q^{5} - 120q^{7} - 64q^{8} + O(q^{10}) \) \( 3q - 4q^{2} + 48q^{4} + 66q^{5} - 120q^{7} - 64q^{8} + 504q^{10} + 60q^{11} - 1326q^{13} - 704q^{14} + 768q^{16} + 414q^{17} - 372q^{19} + 1056q^{20} - 3312q^{22} - 600q^{23} + 13413q^{25} + 2632q^{26} - 1920q^{28} - 5574q^{29} - 12720q^{31} - 1024q^{32} - 6264q^{34} + 11616q^{35} + 3138q^{37} - 3824q^{38} + 8064q^{40} - 19194q^{41} - 16428q^{43} + 960q^{44} + 33120q^{46} + 19680q^{47} + 24363q^{49} - 4924q^{50} - 21216q^{52} + 31266q^{53} - 69768q^{55} - 11264q^{56} + 21528q^{58} - 26340q^{59} + 54474q^{61} + 14368q^{62} + 12288q^{64} - 43428q^{65} + 56508q^{67} + 6624q^{68} - 160128q^{70} - 6120q^{71} - 59178q^{73} + 33832q^{74} - 5952q^{76} + 10560q^{77} + 130560q^{79} + 16896q^{80} + 130536q^{82} + 6468q^{83} - 83268q^{85} - 53264q^{86} - 52992q^{88} + 32742q^{89} - 16944q^{91} - 9600q^{92} + 74880q^{94} + 63096q^{95} + 106206q^{97} - 56676q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
18.6.a.a \(1\) \(2.887\) \(\Q\) None \(-4\) \(0\) \(-96\) \(-148\) \(+\) \(+\) \(q-4q^{2}+2^{4}q^{4}-96q^{5}-148q^{7}+\cdots\)
18.6.a.b \(1\) \(2.887\) \(\Q\) None \(-4\) \(0\) \(66\) \(176\) \(+\) \(-\) \(q-4q^{2}+2^{4}q^{4}+66q^{5}+176q^{7}+\cdots\)
18.6.a.c \(1\) \(2.887\) \(\Q\) None \(4\) \(0\) \(96\) \(-148\) \(-\) \(+\) \(q+4q^{2}+2^{4}q^{4}+96q^{5}-148q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 - 4 T \))
$3$ 1
$5$ (\( 1 + 96 T + 3125 T^{2} \))(\( 1 - 66 T + 3125 T^{2} \))(\( 1 - 96 T + 3125 T^{2} \))
$7$ (\( 1 + 148 T + 16807 T^{2} \))(\( 1 - 176 T + 16807 T^{2} \))(\( 1 + 148 T + 16807 T^{2} \))
$11$ (\( 1 - 384 T + 161051 T^{2} \))(\( 1 - 60 T + 161051 T^{2} \))(\( 1 + 384 T + 161051 T^{2} \))
$13$ (\( 1 + 334 T + 371293 T^{2} \))(\( 1 + 658 T + 371293 T^{2} \))(\( 1 + 334 T + 371293 T^{2} \))
$17$ (\( 1 - 576 T + 1419857 T^{2} \))(\( 1 - 414 T + 1419857 T^{2} \))(\( 1 + 576 T + 1419857 T^{2} \))
$19$ (\( 1 + 664 T + 2476099 T^{2} \))(\( 1 - 956 T + 2476099 T^{2} \))(\( 1 + 664 T + 2476099 T^{2} \))
$23$ (\( 1 + 3840 T + 6436343 T^{2} \))(\( 1 + 600 T + 6436343 T^{2} \))(\( 1 - 3840 T + 6436343 T^{2} \))
$29$ (\( 1 - 96 T + 20511149 T^{2} \))(\( 1 + 5574 T + 20511149 T^{2} \))(\( 1 + 96 T + 20511149 T^{2} \))
$31$ (\( 1 + 4564 T + 28629151 T^{2} \))(\( 1 + 3592 T + 28629151 T^{2} \))(\( 1 + 4564 T + 28629151 T^{2} \))
$37$ (\( 1 - 5798 T + 69343957 T^{2} \))(\( 1 + 8458 T + 69343957 T^{2} \))(\( 1 - 5798 T + 69343957 T^{2} \))
$41$ (\( 1 + 6720 T + 115856201 T^{2} \))(\( 1 + 19194 T + 115856201 T^{2} \))(\( 1 - 6720 T + 115856201 T^{2} \))
$43$ (\( 1 + 14872 T + 147008443 T^{2} \))(\( 1 - 13316 T + 147008443 T^{2} \))(\( 1 + 14872 T + 147008443 T^{2} \))
$47$ (\( 1 + 19200 T + 229345007 T^{2} \))(\( 1 - 19680 T + 229345007 T^{2} \))(\( 1 - 19200 T + 229345007 T^{2} \))
$53$ (\( 1 - 7776 T + 418195493 T^{2} \))(\( 1 - 31266 T + 418195493 T^{2} \))(\( 1 + 7776 T + 418195493 T^{2} \))
$59$ (\( 1 + 13056 T + 714924299 T^{2} \))(\( 1 + 26340 T + 714924299 T^{2} \))(\( 1 - 13056 T + 714924299 T^{2} \))
$61$ (\( 1 - 42782 T + 844596301 T^{2} \))(\( 1 + 31090 T + 844596301 T^{2} \))(\( 1 - 42782 T + 844596301 T^{2} \))
$67$ (\( 1 - 36656 T + 1350125107 T^{2} \))(\( 1 + 16804 T + 1350125107 T^{2} \))(\( 1 - 36656 T + 1350125107 T^{2} \))
$71$ (\( 1 - 64512 T + 1804229351 T^{2} \))(\( 1 + 6120 T + 1804229351 T^{2} \))(\( 1 + 64512 T + 1804229351 T^{2} \))
$73$ (\( 1 + 16810 T + 2073071593 T^{2} \))(\( 1 + 25558 T + 2073071593 T^{2} \))(\( 1 + 16810 T + 2073071593 T^{2} \))
$79$ (\( 1 - 28076 T + 3077056399 T^{2} \))(\( 1 - 74408 T + 3077056399 T^{2} \))(\( 1 - 28076 T + 3077056399 T^{2} \))
$83$ (\( 1 + 66432 T + 3939040643 T^{2} \))(\( 1 - 6468 T + 3939040643 T^{2} \))(\( 1 - 66432 T + 3939040643 T^{2} \))
$89$ (\( 1 + 81792 T + 5584059449 T^{2} \))(\( 1 - 32742 T + 5584059449 T^{2} \))(\( 1 - 81792 T + 5584059449 T^{2} \))
$97$ (\( 1 + 29938 T + 8587340257 T^{2} \))(\( 1 - 166082 T + 8587340257 T^{2} \))(\( 1 + 29938 T + 8587340257 T^{2} \))
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