Properties

Label 315.4.g
Level $315$
Weight $4$
Character orbit 315.g
Rep. character $\chi_{315}(314,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 315.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

Total New Old
Modular forms 152 48 104
Cusp forms 136 48 88
Eisenstein series 16 0 16

Trace form

\( 48 q + 192 q^{4} + O(q^{10}) \) \( 48 q + 192 q^{4} + 768 q^{16} - 432 q^{25} + 816 q^{46} + 456 q^{49} + 7968 q^{64} + 1464 q^{70} + 4368 q^{79} - 1440 q^{85} - 4392 q^{91} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
315.4.g.a 315.g 105.g $48$ $18.586$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)