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Properties

Label 315.3.ca
Level $315$
Weight $3$
Character orbit 315.ca
Rep. character $\chi_{315}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $152$
Newform subspaces $3$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 416 168 248
Cusp forms 352 152 200
Eisenstein series 64 16 48

Trace form

\( 152 q + 2 q^{2} + 10 q^{7} + 12 q^{8} + O(q^{10}) \) \( 152 q + 2 q^{2} + 10 q^{7} + 12 q^{8} - 18 q^{10} + 8 q^{11} - 8 q^{13} + 276 q^{16} - 8 q^{17} + 72 q^{20} - 88 q^{22} + 14 q^{23} + 48 q^{25} + 148 q^{26} + 26 q^{28} - 104 q^{31} - 82 q^{32} + 164 q^{35} - 84 q^{37} + 52 q^{38} - 118 q^{40} - 144 q^{41} - 180 q^{43} - 148 q^{46} - 204 q^{47} - 508 q^{50} + 272 q^{52} + 112 q^{53} - 240 q^{55} + 444 q^{56} - 274 q^{58} - 124 q^{61} + 736 q^{62} - 152 q^{65} + 134 q^{67} + 160 q^{68} - 592 q^{70} + 8 q^{71} - 252 q^{73} + 688 q^{76} - 372 q^{77} - 584 q^{80} + 294 q^{82} - 948 q^{83} + 608 q^{85} - 688 q^{86} - 336 q^{88} - 760 q^{91} + 332 q^{92} - 172 q^{95} - 520 q^{97} - 754 q^{98} + O(q^{100}) \)

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.ca.a 315.ca 35.l $24$ $8.583$ None \(2\) \(0\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
315.3.ca.b 315.ca 35.l $64$ $8.583$ None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
315.3.ca.c 315.ca 35.l $64$ $8.583$ None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{3}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)