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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
225.2.b.a \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2q^{4}+3iq^{7}-2q^{11}+iq^{13}+\cdots\)
225.2.b.b \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+3iq^{8}+4q^{11}+2iq^{13}+\cdots\)
225.2.b.c \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+iq^{7}-iq^{13}+4q^{16}+q^{19}+\cdots\)

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

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