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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
900.6.d.a 900.d 5.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) None 4.6.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+44\beta q^{7}-540 q^{11}-209\beta q^{13}+\cdots\)
900.6.d.b 900.d 5.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) None 60.6.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+22\beta q^{7}-216 q^{11}-385\beta q^{13}+\cdots\)
900.6.d.c 900.d 5.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) None 60.6.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+28\beta q^{7}-156 q^{11}-175\beta q^{13}+\cdots\)
900.6.d.d 900.d 5.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) 900.6.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+211 i q^{7}-427 i q^{13}-3143 q^{19}+\cdots\)
900.6.d.e 900.d 5.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) 36.6.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+118\beta q^{7}-601\beta q^{13}+1432 q^{19}+\cdots\)
900.6.d.f 900.d 5.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) None 60.6.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+122\beta q^{7}+144 q^{11}+25\beta q^{13}+\cdots\)
900.6.d.g 900.d 5.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) None 300.6.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+91 i q^{7}+174 q^{11}+785 i q^{13}+\cdots\)
900.6.d.h 900.d 5.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) None 20.6.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+109\beta q^{7}+480 q^{11}+311\beta q^{13}+\cdots\)
900.6.d.i 900.d 5.b $2$ $144.345$ \(\Q(\sqrt{-1}) \) None 60.6.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+8\beta q^{7}+564 q^{11}-185\beta q^{13}+\cdots\)
900.6.d.j 900.d 5.b $4$ $144.345$ \(\Q(i, \sqrt{7})\) None 300.6.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-11\beta _{1}+\beta _{3})q^{7}+(-186-3\beta _{2}+\cdots)q^{11}+\cdots\)
900.6.d.k 900.d 5.b $4$ $144.345$ \(\Q(i, \sqrt{241})\) None 180.6.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+4\beta _{2})q^{7}+(-120+\beta _{3})q^{11}+\cdots\)
900.6.d.l 900.d 5.b $4$ $144.345$ \(\Q(i, \sqrt{94})\) None 900.6.a.l \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+71\beta _{1}q^{7}+\beta _{3}q^{11}-137\beta _{1}q^{13}+\cdots\)
900.6.d.m 900.d 5.b $4$ $144.345$ \(\Q(i, \sqrt{409})\) None 100.6.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2\beta _{1}+4\beta _{2})q^{7}+(30+\beta _{3})q^{11}+\cdots\)
900.6.d.n 900.d 5.b $4$ $144.345$ \(\Q(i, \sqrt{241})\) None 180.6.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+4\beta _{2})q^{7}+(120-\beta _{3})q^{11}+(8\beta _{1}+\cdots)q^{13}+\cdots\)

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

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