Properties

Label 775.2.f
Level $775$
Weight $2$
Character orbit 775.f
Rep. character $\chi_{775}(557,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $92$
Newform subspaces $7$
Sturm bound $160$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 7 \)
Sturm bound: \(160\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(775, [\chi])\).

Total New Old
Modular forms 172 100 72
Cusp forms 148 92 56
Eisenstein series 24 8 16

Trace form

\( 92 q + 4 q^{2} + 12 q^{7} - 10 q^{8} + O(q^{10}) \) \( 92 q + 4 q^{2} + 12 q^{7} - 10 q^{8} - 40 q^{16} - 16 q^{18} - 38 q^{28} + 4 q^{32} + 44 q^{33} + 16 q^{36} + 38 q^{38} + 24 q^{41} - 24 q^{47} + 40 q^{51} + 104 q^{56} - 44 q^{62} - 40 q^{63} - 104 q^{66} + 12 q^{67} - 48 q^{71} - 98 q^{72} - 24 q^{76} - 104 q^{78} - 28 q^{81} - 34 q^{82} + 20 q^{87} + 60 q^{93} + 72 q^{97} - 46 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
775.2.f.a 775.f 155.f $4$ $6.188$ \(\Q(i, \sqrt{6})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
775.2.f.b 775.f 155.f $4$ $6.188$ \(\Q(i, \sqrt{6})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
775.2.f.c 775.f 155.f $8$ $6.188$ 8.0.3317760000.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}-\beta _{3}q^{3}-4\beta _{2}q^{4}-\beta _{7}q^{6}+\cdots\)
775.2.f.d 775.f 155.f $8$ $6.188$ 8.0.\(\cdots\).2 \(\Q(\sqrt{-155}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{3}q^{3}+2\beta _{4}q^{4}+(-3\beta _{4}-\beta _{7})q^{9}+\cdots\)
775.2.f.e 775.f 155.f $12$ $6.188$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-31}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta _{4}q^{2}+(2\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\beta _{9}+\cdots)q^{7}+\cdots\)
775.2.f.f 775.f 155.f $16$ $6.188$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{7}+\cdots)q^{6}+\cdots\)
775.2.f.g 775.f 155.f $40$ $6.188$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(775, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)