↑

Properties

Label 675.2.w
Level $675$
Weight $2$
Character orbit 675.w
Rep. character $\chi_{675}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $320$
Newform subspaces $2$
Sturm bound $180$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(180\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 768 320 448
Cusp forms 672 320 352
Eisenstein series 96 0 96

Trace form

\( 320 q - 4 q^{7} + O(q^{10}) \) \( 320 q - 4 q^{7} - 4 q^{10} + 20 q^{13} + 80 q^{16} + 20 q^{19} + 44 q^{22} + 8 q^{25} + 64 q^{28} - 80 q^{34} + 56 q^{37} - 60 q^{40} - 52 q^{43} - 52 q^{52} + 4 q^{55} + 24 q^{58} - 80 q^{64} - 32 q^{67} + 40 q^{70} - 20 q^{73} - 40 q^{79} - 132 q^{82} - 260 q^{85} - 44 q^{88} - 320 q^{94} + 100 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
675.2.w.a 675.w 75.l $160$ $5.390$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{20}]$
675.2.w.b 675.w 75.l $160$ $5.390$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{20}]$

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

\( S_{2}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)