Properties

Label 675.2.k
Level $675$
Weight $2$
Character orbit 675.k
Rep. character $\chi_{675}(199,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $3$
Sturm bound $180$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(180\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

Total New Old
Modular forms 216 40 176
Cusp forms 144 32 112
Eisenstein series 72 8 64

Trace form

\( 32 q + 16 q^{4} + O(q^{10}) \) \( 32 q + 16 q^{4} - 10 q^{11} + 18 q^{14} - 16 q^{16} + 8 q^{19} + 56 q^{26} + 14 q^{29} - 8 q^{31} + 18 q^{34} - 26 q^{41} + 8 q^{44} - 6 q^{49} - 60 q^{56} - 2 q^{59} + 10 q^{61} - 44 q^{64} + 64 q^{71} - 40 q^{74} - 14 q^{76} - 22 q^{79} - 28 q^{86} - 132 q^{89} - 4 q^{91} - 42 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
675.2.k.a 675.k 45.j $4$ $5.390$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{4}+3\zeta_{12}q^{7}-3\zeta_{12}^{3}q^{8}+\cdots\)
675.2.k.b 675.k 45.j $12$ $5.390$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{8}q^{2}+(2\beta _{6}-\beta _{9})q^{4}+(-\beta _{3}+\beta _{7}+\cdots)q^{7}+\cdots\)
675.2.k.c 675.k 45.j $16$ $5.390$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(1+\beta _{3}+\beta _{7}+\beta _{11})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)