Properties

Label 144.3.e
Level $144$
Weight $3$
Character orbit 144.e
Rep. character $\chi_{144}(17,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $72$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(7\)
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 4 56
Cusp forms 36 4 32
Eisenstein series 24 0 24

Trace form

\( 4 q - 16 q^{7} + O(q^{10}) \) \( 4 q - 16 q^{7} + 64 q^{19} - 36 q^{25} - 80 q^{31} - 8 q^{37} + 96 q^{43} + 124 q^{49} - 224 q^{55} + 72 q^{61} + 160 q^{67} - 192 q^{73} - 48 q^{79} - 248 q^{85} + 256 q^{91} + 128 q^{97} + O(q^{100}) \)

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.e.a 144.e 3.b $2$ $3.924$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$ \(q+5\beta q^{5}-12q^{7}+4\beta q^{11}-8q^{13}+\cdots\)
144.3.e.b 144.e 3.b $2$ $3.924$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+4q^{7}+4\beta q^{11}+8q^{13}+3\beta q^{17}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)