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Properties

Label 324.5.c
Level $324$
Weight $5$
Character orbit 324.c
Rep. character $\chi_{324}(161,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $270$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(270\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(324, [\chi])\).

Total New Old
Modular forms 234 16 218
Cusp forms 198 16 182
Eisenstein series 36 0 36

Trace form

\( 16 q + 26 q^{7} + O(q^{10}) \) \( 16 q + 26 q^{7} + 230 q^{13} + 254 q^{19} - 1034 q^{25} - 1846 q^{31} + 1244 q^{37} + 524 q^{43} + 4086 q^{49} - 1854 q^{55} + 5678 q^{61} - 2488 q^{67} - 12346 q^{73} - 622 q^{79} + 720 q^{85} + 14074 q^{91} - 17092 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
324.5.c.a 324.c 3.b $8$ $33.492$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(-26\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+(-3+\beta _{3})q^{7}-\beta _{2}q^{11}+\cdots\)
324.5.c.b 324.c 3.b $8$ $33.492$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(52\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+(7-\beta _{1})q^{7}+\beta _{5}q^{11}+(28+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(324, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)