Properties

Label 18.26.a
Level $18$
Weight $26$
Character orbit 18.a
Rep. character $\chi_{18}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $7$
Sturm bound $78$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 18.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(78\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(18))\).

Total New Old
Modular forms 79 10 69
Cusp forms 71 10 61
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
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(5\)

Trace form

\( 10 q + 167772160 q^{4} - 581301684 q^{5} - 10429506640 q^{7} + 2866670075904 q^{10} - 16662482272728 q^{11} + 152073991594940 q^{13} + 53123283025920 q^{14} + 28\!\cdots\!60 q^{16} + 37\!\cdots\!40 q^{17}+ \cdots + 12\!\cdots\!60 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
18.26.a.a 18.a 1.a $1$ $71.279$ \(\Q\) None 6.26.a.c \(-4096\) \(0\) \(799327650\) \(7962409664\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{12}q^{2}+2^{24}q^{4}+799327650q^{5}+\cdots\)
18.26.a.b 18.a 1.a $1$ $71.279$ \(\Q\) None 6.26.a.b \(4096\) \(0\) \(-590425734\) \(57857417576\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{12}q^{2}+2^{24}q^{4}-590425734q^{5}+\cdots\)
18.26.a.c 18.a 1.a $1$ $71.279$ \(\Q\) None 2.26.a.a \(4096\) \(0\) \(-341005350\) \(-40882637368\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{12}q^{2}+2^{24}q^{4}-341005350q^{5}+\cdots\)
18.26.a.d 18.a 1.a $1$ $71.279$ \(\Q\) None 6.26.a.a \(4096\) \(0\) \(292754850\) \(3580644032\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{12}q^{2}+2^{24}q^{4}+292754850q^{5}+\cdots\)
18.26.a.e 18.a 1.a $2$ $71.279$ \(\Q(\sqrt{106705}) \) None 2.26.a.b \(-8192\) \(0\) \(-741953100\) \(-376536944\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{12}q^{2}+2^{24}q^{4}+(-370976550+\cdots)q^{5}+\cdots\)
18.26.a.f 18.a 1.a $2$ $71.279$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 18.26.a.f \(-8192\) \(0\) \(-697960704\) \(-19285401800\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{12}q^{2}+2^{24}q^{4}+(-348980352+\cdots)q^{5}+\cdots\)
18.26.a.g 18.a 1.a $2$ $71.279$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 18.26.a.f \(8192\) \(0\) \(697960704\) \(-19285401800\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{12}q^{2}+2^{24}q^{4}+(348980352+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(18)) \simeq \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)