Properties

Label 315.2.j
Level 315
Weight 2
Character orbit j
Rep. character \(\chi_{315}(46,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 28
Newforms 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: \(\Q(\zeta_{3})\)
Newforms: \( 7 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into irreducible Hecke orbits

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

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