Properties

Label 912.2.f
Level $912$
Weight $2$
Character orbit 912.f
Rep. character $\chi_{912}(113,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $9$
Sturm bound $320$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(320\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

Total New Old
Modular forms 172 42 130
Cusp forms 148 38 110
Eisenstein series 24 4 20

Trace form

\( 38 q + 8 q^{7} + 2 q^{9} + O(q^{10}) \) \( 38 q + 8 q^{7} + 2 q^{9} - 34 q^{25} - 4 q^{39} - 24 q^{43} + 8 q^{45} + 14 q^{49} + 8 q^{55} + 14 q^{57} - 20 q^{61} + 52 q^{63} - 36 q^{73} + 10 q^{81} + 16 q^{85} + 36 q^{87} + 4 q^{93} - 32 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.2.f.a 912.f 57.d $2$ $7.282$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-q^{7}+\cdots\)
912.2.f.b 912.f 57.d $2$ $7.282$ \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta )q^{3}+\beta q^{5}+4q^{7}+(-1+\cdots)q^{9}+\cdots\)
912.2.f.c 912.f 57.d $2$ $7.282$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-8\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{6}q^{3}-4q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
912.2.f.d 912.f 57.d $2$ $7.282$ \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta )q^{3}+\beta q^{5}+4q^{7}+(-1-2\beta )q^{9}+\cdots\)
912.2.f.e 912.f 57.d $2$ $7.282$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}+\cdots\)
912.2.f.f 912.f 57.d $4$ $7.282$ \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2})q^{3}-\beta _{3}q^{5}-q^{7}+(-2+\cdots)q^{9}+\cdots\)
912.2.f.g 912.f 57.d $4$ $7.282$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+q^{7}+(2-\beta _{2})q^{9}+\cdots\)
912.2.f.h 912.f 57.d $10$ $7.282$ 10.0.\(\cdots\).1 None \(0\) \(-1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
912.2.f.i 912.f 57.d $10$ $7.282$ 10.0.\(\cdots\).1 None \(0\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)