Properties

Label 225.2.b
Level $225$
Weight $2$
Character orbit 225.b
Rep. character $\chi_{225}(199,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $60$
Trace bound $4$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 42 8 34
Cusp forms 18 6 12
Eisenstein series 24 2 22

Trace form

\( 6 q + 2 q^{4} + O(q^{10}) \) \( 6 q + 2 q^{4} + 4 q^{11} - 12 q^{14} - 2 q^{16} + 4 q^{19} - 8 q^{26} + 16 q^{29} - 20 q^{31} - 4 q^{34} - 4 q^{41} + 16 q^{44} + 24 q^{46} - 26 q^{49} - 28 q^{59} - 16 q^{61} + 18 q^{64} + 32 q^{71} + 28 q^{74} - 24 q^{76} + 8 q^{79} + 4 q^{86} - 12 q^{89} + 44 q^{91} + 8 q^{94} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.2.b.a 225.b 5.b $2$ $1.797$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+3iq^{7}-2q^{11}+iq^{13}+\cdots\)
225.2.b.b 225.b 5.b $2$ $1.797$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+3iq^{8}+4q^{11}+2iq^{13}+\cdots\)
225.2.b.c 225.b 5.b $2$ $1.797$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+iq^{7}-iq^{13}+4q^{16}+q^{19}+\cdots\)

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

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