Properties

Label 315.2.j
Level $315$
Weight $2$
Character orbit 315.j
Rep. character $\chi_{315}(46,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $7$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).

Total New Old
Modular forms 112 28 84
Cusp forms 80 28 52
Eisenstein series 32 0 32

Trace form

\( 28q - 2q^{2} - 18q^{4} + 2q^{5} + 6q^{7} + 12q^{8} + O(q^{10}) \) \( 28q - 2q^{2} - 18q^{4} + 2q^{5} + 6q^{7} + 12q^{8} - 2q^{10} + 16q^{13} + 8q^{14} - 22q^{16} + 12q^{17} - 4q^{19} - 20q^{20} + 24q^{22} - 10q^{23} - 14q^{25} - 4q^{26} - 14q^{28} + 12q^{29} + 8q^{31} - 14q^{32} - 40q^{34} - 4q^{35} - 12q^{37} - 24q^{38} - 6q^{40} + 12q^{41} - 36q^{43} - 16q^{44} + 22q^{46} + 12q^{47} - 10q^{49} + 4q^{50} - 28q^{52} + 8q^{53} + 24q^{55} + 18q^{56} + 10q^{58} - 12q^{59} + 46q^{61} + 116q^{64} + 8q^{65} + 22q^{67} + 8q^{68} + 14q^{70} - 16q^{71} - 32q^{73} + 4q^{74} - 48q^{76} - 72q^{77} - 4q^{79} + 22q^{80} + 2q^{82} - 12q^{83} + 8q^{85} - 14q^{86} - 76q^{88} - 22q^{89} - 24q^{91} + 76q^{92} + 36q^{94} - 24q^{97} + 14q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
315.2.j.a \(2\) \(2.515\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(1\) \(-1\) \(q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
315.2.j.b \(2\) \(2.515\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(5\) \(q+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
315.2.j.c \(4\) \(2.515\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots\)
315.2.j.d \(4\) \(2.515\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-2\) \(-2\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
315.2.j.e \(4\) \(2.515\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(2\) \(2\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots\)
315.2.j.f \(6\) \(2.515\) 6.0.4406832.1 None \(-2\) \(0\) \(-3\) \(1\) \(q+(-\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
315.2.j.g \(6\) \(2.515\) 6.0.4406832.1 None \(2\) \(0\) \(3\) \(1\) \(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)