Properties

Label 775.2.b
Level $775$
Weight $2$
Character orbit 775.b
Rep. character $\chi_{775}(249,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $8$
Sturm bound $160$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(160\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 86 46 40
Cusp forms 74 46 28
Eisenstein series 12 0 12

Trace form

\( 46 q - 48 q^{4} - 8 q^{6} - 34 q^{9} + O(q^{10}) \) \( 46 q - 48 q^{4} - 8 q^{6} - 34 q^{9} - 12 q^{11} + 2 q^{14} + 68 q^{16} - 8 q^{19} - 28 q^{21} + 28 q^{24} - 28 q^{26} + 16 q^{29} + 6 q^{31} - 52 q^{34} - 28 q^{36} - 4 q^{39} + 60 q^{44} + 20 q^{46} - 10 q^{49} - 36 q^{51} - 24 q^{59} + 12 q^{61} - 110 q^{64} - 4 q^{66} + 32 q^{69} - 16 q^{71} - 12 q^{74} - 22 q^{76} + 64 q^{79} + 22 q^{81} + 76 q^{84} - 64 q^{86} + 44 q^{89} - 72 q^{91} + 32 q^{94} - 52 q^{96} + 136 q^{99} + O(q^{100}) \)

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.b.a 775.b 5.b $2$ $6.188$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots\)
775.2.b.b 775.b 5.b $2$ $6.188$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2iq^{3}+q^{4}-2q^{6}-4iq^{7}+\cdots\)
775.2.b.c 775.b 5.b $2$ $6.188$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2q^{4}+2q^{9}-4q^{11}-2iq^{12}+\cdots\)
775.2.b.d 775.b 5.b $4$ $6.188$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+2\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots\)
775.2.b.e 775.b 5.b $8$ $6.188$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-2+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
775.2.b.f 775.b 5.b $8$ $6.188$ 8.0.4589249536.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{4})q^{4}+(-1+\cdots)q^{6}+\cdots\)
775.2.b.g 775.b 5.b $10$ $6.188$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{4}+\beta _{7})q^{2}+(-\beta _{4}-\beta _{8})q^{3}+(-1+\cdots)q^{4}+\cdots\)
775.2.b.h 775.b 5.b $10$ $6.188$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(-2+\beta _{6}+\cdots)q^{4}+\cdots\)

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

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