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Properties

Label 144.3.g
Level $144$
Weight $3$
Character orbit 144.g
Rep. character $\chi_{144}(127,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $3$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(144, [\chi])\).

Total New Old
Modular forms 60 5 55
Cusp forms 36 5 31
Eisenstein series 24 0 24

Trace form

\( 5 q - 6 q^{5} + O(q^{10}) \) \( 5 q - 6 q^{5} + 26 q^{13} + 42 q^{17} - 17 q^{25} - 102 q^{29} + 34 q^{37} + 90 q^{41} - 235 q^{49} - 54 q^{53} - 14 q^{61} + 228 q^{65} + 146 q^{73} - 288 q^{77} + 108 q^{85} - 150 q^{89} + 194 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.3.g.a 144.g 4.b $1$ $3.924$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+6q^{5}+10q^{13}+30q^{17}+11q^{25}+\cdots\)
144.3.g.b 144.g 4.b $2$ $3.924$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-6q^{5}-\zeta_{6}q^{7}-3\zeta_{6}q^{11}-14q^{13}+\cdots\)
144.3.g.c 144.g 4.b $2$ $3.924$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{7}+22q^{13}-2\zeta_{6}q^{19}-5^{2}q^{25}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)