Properties

Label 225.2.k
Level $225$
Weight $2$
Character orbit 225.k
Rep. character $\chi_{225}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $3$
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.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
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 72 40 32
Cusp forms 48 32 16
Eisenstein series 24 8 16

Trace form

\( 32 q + 16 q^{4} + 8 q^{6} - 2 q^{9} + O(q^{10}) \) \( 32 q + 16 q^{4} + 8 q^{6} - 2 q^{9} + 10 q^{11} - 18 q^{14} - 16 q^{16} + 8 q^{19} - 30 q^{21} + 18 q^{24} - 56 q^{26} - 14 q^{29} - 8 q^{31} + 18 q^{34} + 4 q^{36} - 10 q^{39} + 26 q^{41} - 8 q^{44} - 6 q^{49} - 10 q^{51} - 44 q^{54} + 60 q^{56} + 2 q^{59} + 10 q^{61} - 44 q^{64} - 32 q^{66} - 42 q^{69} - 64 q^{71} + 40 q^{74} - 14 q^{76} - 22 q^{79} - 22 q^{81} + 18 q^{84} + 28 q^{86} + 132 q^{89} - 4 q^{91} - 42 q^{94} + 124 q^{96} + 2 q^{99} + O(q^{100}) \)

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.k.a 225.k 45.j $4$ $1.797$ \(\Q(\zeta_{12})\) None 45.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
225.2.k.b 225.k 45.j $12$ $1.797$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 45.2.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{6}-\beta _{7})q^{2}+\beta _{6}q^{3}+(2+2\beta _{8}+\cdots)q^{4}+\cdots\)
225.2.k.c 225.k 45.j $16$ $1.797$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 225.2.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{10}+\beta _{14})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)

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

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