Properties

Label 945.2.be
Level 945
Weight 2
Character orbit be
Rep. character \(\chi_{945}(206,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 64
Newforms 3
Sturm bound 288
Trace bound 1

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Defining parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(1\)
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 64 248
Cusp forms 264 64 200
Eisenstein series 48 0 48

Trace form

\(64q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 32q^{16} \) \(\mathstrut +\mathstrut 64q^{25} \) \(\mathstrut +\mathstrut 24q^{26} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 120q^{38} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut +\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut -\mathstrut 48q^{53} \) \(\mathstrut -\mathstrut 102q^{56} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 60q^{61} \) \(\mathstrut -\mathstrut 64q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 60q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut +\mathstrut 54q^{77} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 60q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 12q^{92} \) \(\mathstrut -\mathstrut 6q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.be.a \(2\) \(7.546\) \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(-2\) \(-5\) \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
945.2.be.b \(30\) \(7.546\) None \(-3\) \(0\) \(-30\) \(6\)
945.2.be.c \(32\) \(7.546\) None \(0\) \(0\) \(32\) \(1\)

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

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