Properties

Label 945.2.j
Level 945
Weight 2
Character orbit j
Rep. character \(\chi_{945}(541,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 84
Newforms 10
Sturm bound 288
Trace bound 7

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Defining parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 10 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

Total New Old
Modular forms 312 84 228
Cusp forms 264 84 180
Eisenstein series 48 0 48

Trace form

\(84q \) \(\mathstrut -\mathstrut 40q^{4} \) \(\mathstrut -\mathstrut 14q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(84q \) \(\mathstrut -\mathstrut 40q^{4} \) \(\mathstrut -\mathstrut 14q^{7} \) \(\mathstrut -\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 14q^{19} \) \(\mathstrut -\mathstrut 88q^{22} \) \(\mathstrut -\mathstrut 42q^{25} \) \(\mathstrut +\mathstrut 20q^{28} \) \(\mathstrut -\mathstrut 22q^{31} \) \(\mathstrut +\mathstrut 32q^{34} \) \(\mathstrut +\mathstrut 76q^{43} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 32q^{58} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 120q^{64} \) \(\mathstrut +\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 26q^{73} \) \(\mathstrut -\mathstrut 56q^{76} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 8q^{82} \) \(\mathstrut +\mathstrut 144q^{88} \) \(\mathstrut +\mathstrut 64q^{91} \) \(\mathstrut -\mathstrut 56q^{94} \) \(\mathstrut +\mathstrut 36q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
945.2.j.a \(2\) \(7.546\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
945.2.j.b \(2\) \(7.546\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
945.2.j.c \(6\) \(7.546\) 6.0.1783323.2 None \(-1\) \(0\) \(3\) \(-2\) \(q-\beta _{1}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
945.2.j.d \(6\) \(7.546\) 6.0.1783323.2 None \(1\) \(0\) \(-3\) \(-2\) \(q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots\)
945.2.j.e \(10\) \(7.546\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(-5\) \(-5\) \(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{6}+\beta _{9})q^{4}+(-1+\cdots)q^{5}+\cdots\)
945.2.j.f \(10\) \(7.546\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-5\) \(-1\) \(q+(\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{3}+\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots\)
945.2.j.g \(10\) \(7.546\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(5\) \(-5\) \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{6}-\beta _{9})q^{4}+\cdots\)
945.2.j.h \(10\) \(7.546\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(5\) \(-1\) \(q+(-\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
945.2.j.i \(14\) \(7.546\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(-7\) \(2\) \(q+(-\beta _{1}-\beta _{2})q^{2}+(\beta _{3}-\beta _{7}+\beta _{10}+\cdots)q^{4}+\cdots\)
945.2.j.j \(14\) \(7.546\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(7\) \(2\) \(q+(\beta _{1}+\beta _{2})q^{2}+(\beta _{3}-\beta _{7}+\beta _{10})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)