Properties

Label 450.2.c
Level $450$
Weight $2$
Character orbit 450.c
Rep. character $\chi_{450}(199,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $180$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(180\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(450, [\chi])\).

Total New Old
Modular forms 114 8 106
Cusp forms 66 8 58
Eisenstein series 48 0 48

Trace form

\( 8 q - 8 q^{4} + O(q^{10}) \) \( 8 q - 8 q^{4} + 6 q^{11} + 4 q^{14} + 8 q^{16} + 14 q^{19} - 4 q^{26} - 12 q^{29} + 4 q^{31} - 18 q^{34} + 18 q^{41} - 6 q^{44} - 12 q^{46} - 4 q^{56} - 8 q^{61} - 8 q^{64} - 24 q^{71} - 8 q^{74} - 14 q^{76} + 20 q^{79} - 16 q^{86} + 66 q^{89} - 64 q^{91} + 24 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
450.2.c.a 450.c 5.b $2$ $3.593$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-6q^{11}+\cdots\)
450.2.c.b 450.c 5.b $2$ $3.593$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-4iq^{7}-iq^{8}-2iq^{13}+\cdots\)
450.2.c.c 450.c 5.b $2$ $3.593$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+3q^{11}+\cdots\)
450.2.c.d 450.c 5.b $2$ $3.593$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-2iq^{7}-iq^{8}+6q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)