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Properties

Label 225.2.f
Level $225$
Weight $2$
Character orbit 225.f
Rep. character $\chi_{225}(107,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $2$
Sturm bound $60$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(225, [\chi])\).

Total New Old
Modular forms 84 12 72
Cusp forms 36 12 24
Eisenstein series 48 0 48

Trace form

\( 12 q + 8 q^{7} - 4 q^{13} - 28 q^{16} - 8 q^{22} - 8 q^{28} - 8 q^{31} - 4 q^{37} + 32 q^{43} + 32 q^{46} - 4 q^{52} - 12 q^{58} - 24 q^{61} - 16 q^{67} - 4 q^{73} + 160 q^{76} + 4 q^{82} + 24 q^{88} - 88 q^{91}+ \cdots + 44 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.2.f.a 225.f 15.e $4$ $1.797$ \(\Q(\zeta_{8})\) None 45.2.f.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(2-2\zeta_{8}^{2})q^{7}+\cdots\)
225.2.f.b 225.f 15.e $8$ $1.797$ \(\Q(\zeta_{24})\) None 225.2.f.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta_{6} q^{2}-4\beta_{2} q^{4}+\beta_1 q^{7}+2\beta_{4} q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(225, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)