Properties

Label 900.6.d
Level $900$
Weight $6$
Character orbit 900.d
Rep. character $\chi_{900}(649,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $14$
Sturm bound $1080$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(1080\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(900, [\chi])\).

Total New Old
Modular forms 936 38 898
Cusp forms 864 38 826
Eisenstein series 72 0 72

Trace form

\( 38 q + O(q^{10}) \) \( 38 q + 276 q^{11} - 1156 q^{19} + 3924 q^{29} + 1060 q^{31} - 18948 q^{41} - 82746 q^{49} + 9012 q^{59} + 60928 q^{61} - 68664 q^{71} - 25312 q^{79} + 162852 q^{89} + 224924 q^{91} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
900.6.d.a $2$ $144.345$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+44iq^{7}-540q^{11}-209iq^{13}+\cdots\)
900.6.d.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+22iq^{7}-6^{3}q^{11}-385iq^{13}-267iq^{17}+\cdots\)
900.6.d.c $2$ $144.345$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+28iq^{7}-156q^{11}-175iq^{13}+\cdots\)
900.6.d.d $2$ $144.345$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+211iq^{7}-427iq^{13}-3143q^{19}+\cdots\)
900.6.d.e $2$ $144.345$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+118iq^{7}-601iq^{13}+1432q^{19}+\cdots\)
900.6.d.f $2$ $144.345$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+122iq^{7}+12^{2}q^{11}+5^{2}iq^{13}+\cdots\)
900.6.d.g $2$ $144.345$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+91iq^{7}+174q^{11}+785iq^{13}+\cdots\)
900.6.d.h $2$ $144.345$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+109iq^{7}+480q^{11}+311iq^{13}+\cdots\)
900.6.d.i $2$ $144.345$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+8iq^{7}+564q^{11}-185iq^{13}-543iq^{17}+\cdots\)
900.6.d.j $4$ $144.345$ \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-11\beta _{1}+\beta _{3})q^{7}+(-186-3\beta _{2}+\cdots)q^{11}+\cdots\)
900.6.d.k $4$ $144.345$ \(\Q(i, \sqrt{241})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+4\beta _{2})q^{7}+(-120+\beta _{3})q^{11}+\cdots\)
900.6.d.l $4$ $144.345$ \(\Q(i, \sqrt{94})\) None \(0\) \(0\) \(0\) \(0\) \(q+71\beta _{1}q^{7}+\beta _{3}q^{11}-137\beta _{1}q^{13}+\cdots\)
900.6.d.m $4$ $144.345$ \(\Q(i, \sqrt{409})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-2\beta _{1}+4\beta _{2})q^{7}+(30+\beta _{3})q^{11}+\cdots\)
900.6.d.n $4$ $144.345$ \(\Q(i, \sqrt{241})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+4\beta _{2})q^{7}+(120-\beta _{3})q^{11}+(8\beta _{1}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)