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Properties

Label 270.4.f
Level $270$
Weight $4$
Character orbit 270.f
Rep. character $\chi_{270}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $2$
Sturm bound $216$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 270.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(270, [\chi])\).

Total New Old
Modular forms 348 48 300
Cusp forms 300 48 252
Eisenstein series 48 0 48

Trace form

\( 48 q + 12 q^{7} + O(q^{10}) \) \( 48 q + 12 q^{7} + 24 q^{10} - 48 q^{13} - 768 q^{16} + 312 q^{22} - 72 q^{25} + 48 q^{28} - 504 q^{31} - 312 q^{37} + 384 q^{40} + 2064 q^{43} - 144 q^{46} + 192 q^{52} - 12 q^{55} - 3552 q^{58} + 1920 q^{61} + 696 q^{67} - 2616 q^{70} + 396 q^{73} - 1152 q^{76} - 1536 q^{82} + 4104 q^{85} + 1248 q^{88} + 10416 q^{91} - 1404 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(270, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
270.4.f.a 270.f 15.e $24$ $15.931$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{4}]$
270.4.f.b 270.f 15.e $24$ $15.931$ None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(270, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(270, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)