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Properties

Label 18.34.a
Level $18$
Weight $34$
Character orbit 18.a
Rep. character $\chi_{18}(1,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $8$
Sturm bound $102$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 34 \)
Character orbit: \([\chi]\) \(=\) 18.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(102\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_0(18))\).

Total New Old
Modular forms 103 14 89
Cusp forms 95 14 81
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
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(4\)
\(-\)\(+\)$-$\(3\)
\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(7\)
Minus space\(-\)\(7\)

Trace form

\( 14 q + 60129542144 q^{4} - 304056133344 q^{5} + 117312920451928 q^{7} + O(q^{10}) \) \( 14 q + 60129542144 q^{4} - 304056133344 q^{5} + 117312920451928 q^{7} + 14602515202965504 q^{10} - 132277758256645200 q^{11} + 1461874643704935388 q^{13} - 8817945522116493312 q^{14} + 258254417031933722624 q^{16} - 607761009550907238384 q^{17} + 2454979321645799580064 q^{19} - 1305911148860695117824 q^{20} - 6631576866819554672640 q^{22} + 67550213002417622816256 q^{23} - 2340137875112737027942 q^{25} + 132678853336547098361856 q^{26} + 503855156739280300146688 q^{28} - 2456674447349242602600192 q^{29} + 2388697736170083638704120 q^{31} + 3658862187782745995870208 q^{34} + 29284367614103118458807136 q^{35} + 7396543777047510265889716 q^{37} - 7348400553398410930028544 q^{38} + 62717325236079641896157184 q^{40} - 330794197002844183788005232 q^{41} - 1667440831236615022931117504 q^{43} - 568128645700485108675379200 q^{44} + 3686497542248495353901875200 q^{46} - 974731800450682494683775648 q^{47} + 11439850896723631384728331134 q^{49} - 168281807483933081336807424 q^{50} + 6278703785564349765253070848 q^{52} - 52552641452740799417838246528 q^{53} + 56151711662109507413789422752 q^{55} - 37872787635399983477242724352 q^{56} - 7516347832431374878157832192 q^{58} - 542558844048585466098142556400 q^{59} + 340069888623815129266733312452 q^{61} - 285749892967457392664430772224 q^{62} + 1109194275199700726309615304704 q^{64} - 2975697566808532038448806987648 q^{65} + 4142275100748846576784467841456 q^{67} - 2610313659805090235988955889664 q^{68} + 2736534347549001881946635108352 q^{70} - 19870385005723060698640836667200 q^{71} + 16408219680629761475245691782036 q^{73} - 16437943549597071583171307372544 q^{74} + 10544055898824974092145413586944 q^{76} - 54148811505285243597031893347136 q^{77} + 58495545652569274169543872355320 q^{79} - 5608845675838473190880946683904 q^{80} - 3767881004467431543236085153792 q^{82} - 145395420968178029578615362564336 q^{83} + 113840491583047071823710599377152 q^{85} - 110477938400502767650695190413312 q^{86} - 28482405763900134852272785981440 q^{88} + 36294220976456682462294451209456 q^{89} - 22257446986199745849969327614992 q^{91} + 290125955683217658929882937163776 q^{92} - 228886467829527255537892196352000 q^{94} + 1790842943334582998101299903153696 q^{95} - 2415527744472227678923330324629596 q^{97} + 1521114936804038504336395560026112 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_0(18))\) 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
18.34.a.a 18.a 1.a $1$ $124.169$ \(\Q\) None \(-65536\) \(0\) \(-397843662750\) \(-19\!\cdots\!36\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{16}q^{2}+2^{32}q^{4}-397843662750q^{5}+\cdots\)
18.34.a.b 18.a 1.a $1$ $124.169$ \(\Q\) None \(-65536\) \(0\) \(249151856250\) \(-32\!\cdots\!12\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{16}q^{2}+2^{32}q^{4}+249151856250q^{5}+\cdots\)
18.34.a.c 18.a 1.a $1$ $124.169$ \(\Q\) None \(65536\) \(0\) \(-538799132550\) \(-33\!\cdots\!68\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{16}q^{2}+2^{32}q^{4}-538799132550q^{5}+\cdots\)
18.34.a.d 18.a 1.a $1$ $124.169$ \(\Q\) None \(65536\) \(0\) \(368836145250\) \(16\!\cdots\!32\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{16}q^{2}+2^{32}q^{4}+368836145250q^{5}+\cdots\)
18.34.a.e 18.a 1.a $2$ $124.169$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-131072\) \(0\) \(5332476660\) \(13\!\cdots\!56\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{16}q^{2}+2^{32}q^{4}+(2666238330+\cdots)q^{5}+\cdots\)
18.34.a.f 18.a 1.a $2$ $124.169$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(131072\) \(0\) \(9266183796\) \(-37\!\cdots\!48\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{16}q^{2}+2^{32}q^{4}+(4633091898+\cdots)q^{5}+\cdots\)
18.34.a.g 18.a 1.a $3$ $124.169$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-196608\) \(0\) \(-120077086464\) \(45\!\cdots\!52\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{16}q^{2}+2^{32}q^{4}+(-40025695488+\cdots)q^{5}+\cdots\)
18.34.a.h 18.a 1.a $3$ $124.169$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(196608\) \(0\) \(120077086464\) \(45\!\cdots\!52\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{16}q^{2}+2^{32}q^{4}+(40025695488+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)