↑

Properties

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

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
18.6.a.a 18.a 1.a $1$ $2.887$ \(\Q\) None \(-4\) \(0\) \(-96\) \(-148\) $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+2^{4}q^{4}-96q^{5}-148q^{7}+\cdots\)
18.6.a.b 18.a 1.a $1$ $2.887$ \(\Q\) None \(-4\) \(0\) \(66\) \(176\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+2^{4}q^{4}+66q^{5}+176q^{7}+\cdots\)
18.6.a.c 18.a 1.a $1$ $2.887$ \(\Q\) None \(4\) \(0\) \(96\) \(-148\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+2^{4}q^{4}+96q^{5}-148q^{7}+\cdots\)

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

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