Properties

Label 18.16.a
Level $18$
Weight $16$
Character orbit 18.a
Rep. character $\chi_{18}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $6$
Sturm bound $48$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 18.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(18))\).

Total New Old
Modular forms 49 6 43
Cusp forms 41 6 35
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(3\)

Trace form

\( 6 q + 98304 q^{4} + 261144 q^{5} + 6924216 q^{7} + O(q^{10}) \) \( 6 q + 98304 q^{4} + 261144 q^{5} + 6924216 q^{7} - 43425792 q^{10} + 41075424 q^{11} - 254112756 q^{13} + 550084608 q^{14} + 1610612736 q^{16} + 5461900632 q^{17} - 5167009968 q^{19} + 4278583296 q^{20} - 25768304640 q^{22} - 2612038752 q^{23} + 81580872066 q^{25} - 23615815680 q^{26} + 113446354944 q^{28} - 257198248296 q^{29} - 408938462664 q^{31} - 156675686400 q^{34} + 229286306016 q^{35} + 1636049157492 q^{37} + 884208918528 q^{38} - 711488176128 q^{40} + 2048853252600 q^{41} - 4873382203632 q^{43} + 672979746816 q^{44} + 1481812180992 q^{46} - 9705384160416 q^{47} + 11120052363606 q^{49} + 11249380196352 q^{50} - 4163383394304 q^{52} - 25540321761864 q^{53} + 6844247235072 q^{55} + 9012586217472 q^{56} - 21753679896576 q^{58} - 32598503680320 q^{59} - 23063727716700 q^{61} + 96763632279552 q^{62} + 26388279066624 q^{64} - 11084081113008 q^{65} + 96029925375072 q^{67} + 89487779954688 q^{68} - 107772857008128 q^{70} - 135158267441376 q^{71} - 30680860304652 q^{73} + 251213352763392 q^{74} - 84656291315712 q^{76} - 573783871269312 q^{77} - 32535586725000 q^{79} + 70100308721664 q^{80} + 307010001125376 q^{82} - 374096416055328 q^{83} + 737242480903824 q^{85} + 444207160664064 q^{86} - 422187903221760 q^{88} + 285108615969048 q^{89} - 898479641616528 q^{91} - 42795642912768 q^{92} - 742495624740864 q^{94} + 1362054542256000 q^{95} - 520503457299612 q^{97} - 728103793065984 q^{98} + O(q^{100}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
18.16.a.a $1$ $25.685$ \(\Q\) None \(-128\) \(0\) \(-77646\) \(762104\) $+$ $-$ \(q-2^{7}q^{2}+2^{14}q^{4}-77646q^{5}+762104q^{7}+\cdots\)
18.16.a.b $1$ $25.685$ \(\Q\) None \(-128\) \(0\) \(114810\) \(-3034528\) $+$ $-$ \(q-2^{7}q^{2}+2^{14}q^{4}+114810q^{5}-3034528q^{7}+\cdots\)
18.16.a.c $1$ $25.685$ \(\Q\) None \(-128\) \(0\) \(263040\) \(3585764\) $+$ $+$ \(q-2^{7}q^{2}+2^{14}q^{4}+263040q^{5}+3585764q^{7}+\cdots\)
18.16.a.d $1$ $25.685$ \(\Q\) None \(128\) \(0\) \(-263040\) \(3585764\) $-$ $+$ \(q+2^{7}q^{2}+2^{14}q^{4}-263040q^{5}+3585764q^{7}+\cdots\)
18.16.a.e $1$ $25.685$ \(\Q\) None \(128\) \(0\) \(-90510\) \(56\) $-$ $-$ \(q+2^{7}q^{2}+2^{14}q^{4}-90510q^{5}+56q^{7}+\cdots\)
18.16.a.f $1$ $25.685$ \(\Q\) None \(128\) \(0\) \(314490\) \(2025056\) $-$ $-$ \(q+2^{7}q^{2}+2^{14}q^{4}+314490q^{5}+2025056q^{7}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)