Properties

Label 675.3.d
Level $675$
Weight $3$
Character orbit 675.d
Rep. character $\chi_{675}(674,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $12$
Sturm bound $270$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 675.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(270\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(675, [\chi])\).

Total New Old
Modular forms 198 48 150
Cusp forms 162 48 114
Eisenstein series 36 0 36

Trace form

\( 48 q + 100 q^{4} + 140 q^{16} + 50 q^{19} + 134 q^{31} + 196 q^{34} + 216 q^{46} - 586 q^{49} - 518 q^{61} + 672 q^{64} + 1068 q^{76} + 256 q^{79} - 230 q^{91} - 812 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
675.3.d.a 675.d 15.d $2$ $18.392$ \(\Q(\sqrt{-1}) \) None 27.3.b.b \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 q^{2}+5 q^{4}+\beta q^{7}-3 q^{8}-3\beta q^{11}+\cdots\)
675.3.d.b 675.d 15.d $2$ $18.392$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) 675.3.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-4 q^{4}+2 i q^{7}+i q^{13}+16 q^{16}+\cdots\)
675.3.d.c 675.d 15.d $2$ $18.392$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) 27.3.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-4 q^{4}-13 i q^{7}+i q^{13}+16 q^{16}+\cdots\)
675.3.d.d 675.d 15.d $2$ $18.392$ \(\Q(\sqrt{-1}) \) None 27.3.b.b \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 q^{2}+5 q^{4}+\beta q^{7}+3 q^{8}+3\beta q^{11}+\cdots\)
675.3.d.e 675.d 15.d $4$ $18.392$ \(\Q(i, \sqrt{5})\) None 135.3.c.c \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+(-2-3\beta _{2})q^{4}+3\beta _{1}q^{7}+\cdots\)
675.3.d.f 675.d 15.d $4$ $18.392$ \(\Q(i, \sqrt{5})\) None 135.3.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+q^{4}+12\beta _{1}q^{7}-3\beta _{3}q^{8}+\cdots\)
675.3.d.g 675.d 15.d $4$ $18.392$ \(\Q(i, \sqrt{5})\) None 675.3.c.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+q^{4}+3\beta _{1}q^{7}-3\beta _{3}q^{8}+\cdots\)
675.3.d.h 675.d 15.d $4$ $18.392$ \(\Q(i, \sqrt{11})\) None 675.3.c.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+7q^{4}+9\beta _{1}q^{7}+3\beta _{2}q^{8}+\cdots\)
675.3.d.i 675.d 15.d $4$ $18.392$ \(\Q(i, \sqrt{5})\) None 135.3.c.c \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{2})q^{2}+(-2-3\beta _{2})q^{4}+3\beta _{1}q^{7}+\cdots\)
675.3.d.j 675.d 15.d $6$ $18.392$ 6.0.60217600.1 None 675.3.c.r \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+(2-2\beta _{2}-\beta _{4})q^{4}+\cdots\)
675.3.d.k 675.d 15.d $6$ $18.392$ 6.0.60217600.1 None 675.3.c.r \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{2})q^{2}+(2-2\beta _{2}-\beta _{4})q^{4}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
675.3.d.l 675.d 15.d $8$ $18.392$ 8.0.\(\cdots\).1 None 135.3.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(4+\beta _{6})q^{4}+(-\beta _{2}+4\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(675, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)