Properties

Label 945.2.d
Level $945$
Weight $2$
Character orbit 945.d
Rep. character $\chi_{945}(379,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $6$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

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

Total New Old
Modular forms 156 48 108
Cusp forms 132 48 84
Eisenstein series 24 0 24

Trace form

\( 48 q - 52 q^{4} + O(q^{10}) \) \( 48 q - 52 q^{4} + 24 q^{10} + 44 q^{16} + 16 q^{25} + 16 q^{31} - 12 q^{34} - 56 q^{40} - 28 q^{46} - 48 q^{49} + 4 q^{55} + 96 q^{61} + 16 q^{64} - 8 q^{70} - 44 q^{76} - 76 q^{85} - 184 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
945.2.d.a 945.d 5.b $2$ $7.546$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(-1-2i)q^{5}-iq^{7}+\cdots\)
945.2.d.b 945.d 5.b $2$ $7.546$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(1-2i)q^{5}+iq^{7}+3iq^{8}+\cdots\)
945.2.d.c 945.d 5.b $8$ $7.546$ 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{4})q^{4}+(-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
945.2.d.d 945.d 5.b $10$ $7.546$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{3}q^{5}-\beta _{5}q^{7}+\cdots\)
945.2.d.e 945.d 5.b $10$ $7.546$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{4}q^{5}+\beta _{5}q^{7}+\cdots\)
945.2.d.f 945.d 5.b $16$ $7.546$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}+(-2-\beta _{7})q^{4}-\beta _{9}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)