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Properties

Label 12.18.a
Level $12$
Weight $18$
Character orbit 12.a
Rep. character $\chi_{12}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $36$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 12.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(12))\).

Total New Old
Modular forms 37 2 35
Cusp forms 31 2 29
Eisenstein series 6 0 6

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
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(1\)

Trace form

\( 2 q - 1477980 q^{5} - 24263960 q^{7} + 86093442 q^{9} + O(q^{10}) \) \( 2 q - 1477980 q^{5} - 24263960 q^{7} + 86093442 q^{9} - 1032380208 q^{11} - 874027700 q^{13} + 11415352680 q^{15} + 43735163220 q^{17} - 153568558640 q^{19} - 35623553112 q^{21} - 80527437360 q^{23} + 1079924741150 q^{25} - 2282551050492 q^{29} + 2168009129608 q^{31} - 4320806648760 q^{33} + 13207404535920 q^{35} - 38816475554900 q^{37} + 28716563238480 q^{39} + 17740604240100 q^{41} + 97730802970480 q^{43} - 63622192703580 q^{45} - 172678557920400 q^{47} - 156150915890382 q^{49} - 287565080446512 q^{51} + 1087043089943700 q^{53} + 190011694259520 q^{55} + 259956087018840 q^{57} - 182503267515072 q^{59} - 2937122125020356 q^{61} - 1044483916475160 q^{63} + 4453501300162200 q^{65} - 669199133977280 q^{67} - 4345109590241952 q^{69} + 12010628577638160 q^{71} - 1309673501636780 q^{73} - 16871662953986400 q^{75} + 14312669809183200 q^{77} - 12372197413768664 q^{79} + 3706040377703682 q^{81} + 43379661699213840 q^{83} - 70448847823448280 q^{85} - 33328475346849480 q^{87} + 98415339645711060 q^{89} - 1278589146387280 q^{91} - 86131414373528520 q^{93} + 147953880687427200 q^{95} - 9941979634166300 q^{97} - 44440582779697968 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(12))\) 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
12.18.a.a 12.a 1.a $1$ $21.987$ \(\Q\) None \(0\) \(-6561\) \(-1608930\) \(-9417184\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{8}q^{3}-1608930q^{5}-9417184q^{7}+\cdots\)
12.18.a.b 12.a 1.a $1$ $21.987$ \(\Q\) None \(0\) \(6561\) \(130950\) \(-14846776\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{8}q^{3}+130950q^{5}-14846776q^{7}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)