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Properties

Label 2268.4.f
Level $2268$
Weight $4$
Character orbit 2268.f
Rep. character $\chi_{2268}(1133,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $2$
Sturm bound $1728$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2268.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(1728\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2268, [\chi])\).

Total New Old
Modular forms 1332 96 1236
Cusp forms 1260 96 1164
Eisenstein series 72 0 72

Trace form

\( 96 q + 12 q^{7} + O(q^{10}) \) \( 96 q + 12 q^{7} + 2400 q^{25} - 336 q^{37} + 1176 q^{43} - 444 q^{49} + 840 q^{67} + 2280 q^{79} + 2736 q^{85} - 1728 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2268, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2268.4.f.a 2268.f 21.c $48$ $133.816$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$
2268.4.f.b 2268.f 21.c $48$ $133.816$ None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(2268, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1134, [\chi])\)\(^{\oplus 2}\)