Properties

Label 450.2.e
Level $450$
Weight $2$
Character orbit 450.e
Rep. character $\chi_{450}(151,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $38$
Newform subspaces $14$
Sturm bound $180$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(180\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 204 38 166
Cusp forms 156 38 118
Eisenstein series 48 0 48

Trace form

\( 38 q - q^{2} + q^{3} - 19 q^{4} - 5 q^{6} - 2 q^{7} + 2 q^{8} - 5 q^{9} - q^{11} + 4 q^{12} - 2 q^{13} + 2 q^{14} - 19 q^{16} + 18 q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{21} + 3 q^{22} + 6 q^{23} + q^{24}+ \cdots - 88 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
450.2.e.a 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None 450.2.e.a \(-1\) \(-3\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.b 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None 90.2.i.a \(-1\) \(-3\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.c 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None 450.2.e.c \(-1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.d 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None 90.2.e.b \(-1\) \(3\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.e 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None 90.2.e.a \(1\) \(-3\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.f 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None 450.2.e.c \(1\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.g 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None 90.2.i.a \(1\) \(3\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.h 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None 450.2.e.a \(1\) \(3\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.i 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None 18.2.c.a \(1\) \(3\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.j 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 90.2.e.c \(-2\) \(-2\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
450.2.e.k 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 90.2.i.b \(-2\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
450.2.e.l 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 450.2.e.l \(-2\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
450.2.e.m 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 450.2.e.l \(2\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}+(-1+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
450.2.e.n 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 90.2.i.b \(2\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(450, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)