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Properties

Label 315.3.x
Level $315$
Weight $3$
Character orbit 315.x
Rep. character $\chi_{315}(76,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(315, [\chi])\).

Total New Old
Modular forms 200 128 72
Cusp forms 184 128 56
Eisenstein series 16 0 16

Trace form

\( 128 q - 128 q^{4} - 2 q^{7} + 20 q^{9} + O(q^{10}) \) \( 128 q - 128 q^{4} - 2 q^{7} + 20 q^{9} - 6 q^{11} - 42 q^{14} + 10 q^{15} - 256 q^{16} - 68 q^{18} + 30 q^{21} + 36 q^{23} + 320 q^{25} + 32 q^{28} + 36 q^{29} - 40 q^{30} + 360 q^{32} - 288 q^{36} - 88 q^{37} + 90 q^{39} + 330 q^{42} + 128 q^{43} - 168 q^{44} + 48 q^{46} + 50 q^{49} - 150 q^{51} - 336 q^{53} - 594 q^{56} - 60 q^{57} - 60 q^{60} + 176 q^{63} + 1024 q^{64} + 30 q^{65} - 140 q^{67} - 60 q^{70} + 96 q^{71} + 1532 q^{72} + 708 q^{74} - 234 q^{77} - 60 q^{78} - 62 q^{79} + 92 q^{81} - 798 q^{84} - 30 q^{85} + 156 q^{86} + 564 q^{91} - 816 q^{92} - 1020 q^{93} + 504 q^{98} - 1328 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
315.3.x.a 315.x 63.l $128$ $8.583$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)