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Properties

Label 675.2.u
Level $675$
Weight $2$
Character orbit 675.u
Rep. character $\chi_{675}(49,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $312$
Newform subspaces $5$
Sturm bound $180$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.u (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 5 \)
Sturm bound: \(180\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

Total New Old
Modular forms 576 336 240
Cusp forms 504 312 192
Eisenstein series 72 24 48

Trace form

\( 312 q + 12 q^{4} - 24 q^{6} + 24 q^{9} + O(q^{10}) \) \( 312 q + 12 q^{4} - 24 q^{6} + 24 q^{9} - 24 q^{11} + 24 q^{14} + 6 q^{19} - 48 q^{21} - 6 q^{24} - 96 q^{26} + 48 q^{29} + 6 q^{31} - 96 q^{36} + 30 q^{39} - 12 q^{41} - 102 q^{44} - 6 q^{46} + 48 q^{49} - 54 q^{51} - 192 q^{54} + 138 q^{56} + 42 q^{59} - 48 q^{61} + 120 q^{64} + 174 q^{66} - 60 q^{69} + 78 q^{71} - 138 q^{74} + 12 q^{76} - 60 q^{79} - 186 q^{84} - 42 q^{86} - 36 q^{89} - 6 q^{91} - 60 q^{94} - 168 q^{96} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
675.2.u.a 675.u 135.p $12$ $5.390$ \(\Q(\zeta_{36})\) None 675.2.l.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-\zeta_{36}^{5}+\zeta_{36}^{7}-\zeta_{36}^{9})q^{2}+(-2\zeta_{36}^{5}+\cdots)q^{3}+\cdots\)
675.2.u.b 675.u 135.p $24$ $5.390$ None 27.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
675.2.u.c 675.u 135.p $60$ $5.390$ None 135.2.k.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
675.2.u.d 675.u 135.p $84$ $5.390$ None 135.2.k.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
675.2.u.e 675.u 135.p $132$ $5.390$ None 675.2.l.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)