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Properties

Label 225.4.k
Level $225$
Weight $4$
Character orbit 225.k
Rep. character $\chi_{225}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $104$
Newform subspaces $5$
Sturm bound $120$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(225, [\chi])\).

Total New Old
Modular forms 192 112 80
Cusp forms 168 104 64
Eisenstein series 24 8 16

Trace form

\( 104 q + 202 q^{4} - 4 q^{6} + 64 q^{9} + O(q^{10}) \) \( 104 q + 202 q^{4} - 4 q^{6} + 64 q^{9} - 98 q^{11} - 6 q^{14} - 754 q^{16} + 8 q^{19} - 78 q^{21} - 510 q^{24} + 1192 q^{26} + 682 q^{29} + 34 q^{31} - 378 q^{34} - 128 q^{36} - 58 q^{39} - 502 q^{41} - 4664 q^{44} + 1104 q^{46} + 2358 q^{49} + 68 q^{51} + 6682 q^{54} - 2052 q^{56} + 1964 q^{59} + 34 q^{61} - 6512 q^{64} + 8254 q^{66} - 1026 q^{69} + 2240 q^{71} + 4612 q^{74} - 1214 q^{76} + 686 q^{79} + 440 q^{81} - 5682 q^{84} - 9494 q^{86} - 10272 q^{89} + 2372 q^{91} + 402 q^{94} - 17516 q^{96} - 136 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.4.k.a 225.k 45.j $8$ $13.275$ 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{7}q^{2}+(3\beta _{1}+\beta _{4}+2\beta _{5}+2\beta _{7})q^{3}+\cdots\)
225.4.k.b 225.k 45.j $8$ $13.275$ 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{7})q^{2}+(\beta _{4}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
225.4.k.c 225.k 45.j $12$ $13.275$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{7}+\beta _{11})q^{2}+(\beta _{5}+\beta _{8}+\beta _{11})q^{3}+\cdots\)
225.4.k.d 225.k 45.j $28$ $13.275$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
225.4.k.e 225.k 45.j $48$ $13.275$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

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