Properties

Label 900.2.o
Level $900$
Weight $2$
Character orbit 900.o
Rep. character $\chi_{900}(299,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $208$
Newform subspaces $4$
Sturm bound $360$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 900.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(360\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(900, [\chi])\).

Total New Old
Modular forms 384 224 160
Cusp forms 336 208 128
Eisenstein series 48 16 32

Trace form

\( 208 q + 2 q^{4} + 8 q^{9} + O(q^{10}) \) \( 208 q + 2 q^{4} + 8 q^{9} + 6 q^{14} - 2 q^{16} - 28 q^{21} + 46 q^{24} + 36 q^{29} + 10 q^{34} - 12 q^{41} - 24 q^{46} - 76 q^{49} + 14 q^{54} - 132 q^{56} - 4 q^{61} + 32 q^{64} - 122 q^{66} + 12 q^{69} - 24 q^{74} + 18 q^{76} - 14 q^{84} - 174 q^{86} + 18 q^{94} - 120 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
900.2.o.a 900.o 180.n $16$ $7.187$ 16.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+(-\beta _{5}-\beta _{14}-\beta _{15})q^{3}+\cdots\)
900.2.o.b 900.o 180.n $48$ $7.187$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
900.2.o.c 900.o 180.n $48$ $7.187$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
900.2.o.d 900.o 180.n $96$ $7.187$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)