Properties

Label 162.7.b
Level $162$
Weight $7$
Character orbit 162.b
Rep. character $\chi_{162}(161,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $3$
Sturm bound $189$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 162.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(189\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(162, [\chi])\).

Total New Old
Modular forms 174 24 150
Cusp forms 150 24 126
Eisenstein series 24 0 24

Trace form

\( 24 q - 768 q^{4} + 480 q^{7} + O(q^{10}) \) \( 24 q - 768 q^{4} + 480 q^{7} + 1872 q^{10} + 5016 q^{13} + 24576 q^{16} - 16260 q^{19} + 7200 q^{22} - 74280 q^{25} - 15360 q^{28} - 6000 q^{31} + 62640 q^{34} - 57084 q^{37} - 59904 q^{40} - 184524 q^{43} - 135072 q^{46} + 1099512 q^{49} - 160512 q^{52} + 69336 q^{55} + 573552 q^{58} + 10092 q^{61} - 786432 q^{64} + 284196 q^{67} - 480096 q^{70} - 2641092 q^{73} + 520320 q^{76} - 646008 q^{79} + 620064 q^{82} - 743796 q^{85} - 230400 q^{88} + 1521168 q^{91} - 518112 q^{94} + 1499412 q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.7.b.a 162.b 3.b $4$ $37.269$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 162.7.b.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-4\beta _{1}q^{2}-2^{5}q^{4}+(70\beta _{1}-5^{2}\beta _{2}+\cdots)q^{5}+\cdots\)
162.7.b.b 162.b 3.b $8$ $37.269$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 162.7.b.b \(0\) \(0\) \(0\) \(964\) $\mathrm{SU}(2)[C_{2}]$ \(q+4\beta _{1}q^{2}-2^{5}q^{4}+(12\beta _{1}+\beta _{3})q^{5}+\cdots\)
162.7.b.c 162.b 3.b $12$ $37.269$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 18.7.d.a \(0\) \(0\) \(0\) \(-480\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-2^{5}q^{4}+\beta _{8}q^{5}+(-40-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)