Properties

Label 845.2.c
Level $845$
Weight $2$
Character orbit 845.c
Rep. character $\chi_{845}(506,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $8$
Sturm bound $182$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(182\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(845, [\chi])\).

Total New Old
Modular forms 106 50 56
Cusp forms 78 50 28
Eisenstein series 28 0 28

Trace form

\( 50 q + 4 q^{3} - 46 q^{4} + 50 q^{9} - 2 q^{10} - 12 q^{14} + 46 q^{16} - 4 q^{17} + 20 q^{22} - 16 q^{23} - 50 q^{25} + 28 q^{27} - 20 q^{30} + 4 q^{35} - 2 q^{36} + 44 q^{38} + 6 q^{40} - 64 q^{42} - 24 q^{43}+ \cdots - 16 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(845, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
845.2.c.a 845.c 13.b $2$ $6.747$ \(\Q(\sqrt{-1}) \) None 65.2.a.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-2 q^{3}+q^{4}+i q^{5}-2 i q^{6}+\cdots\)
845.2.c.b 845.c 13.b $4$ $6.747$ \(\Q(\zeta_{8})\) None 65.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta_{2}+\beta_1)q^{2}-\beta_{3} q^{3}+(-2\beta_{3}-1)q^{4}+\cdots\)
845.2.c.c 845.c 13.b $4$ $6.747$ \(\Q(i, \sqrt{5})\) None 65.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+2\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
845.2.c.d 845.c 13.b $4$ $6.747$ \(\Q(i, \sqrt{13})\) None 65.2.e.b \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
845.2.c.e 845.c 13.b $4$ $6.747$ \(\Q(\zeta_{12})\) None 65.2.a.c \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{2} q^{2}+(-\beta_{3}+1)q^{3}-q^{4}+\beta_1 q^{5}+\cdots\)
845.2.c.f 845.c 13.b $6$ $6.747$ 6.0.153664.1 None 845.2.a.h \(0\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
845.2.c.g 845.c 13.b $8$ $6.747$ 8.0.22581504.2 None 65.2.m.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.c.h 845.c 13.b $18$ $6.747$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 845.2.a.n \(0\) \(14\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{6})q^{2}+(1+\beta _{11})q^{3}+(-2+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(845, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(845, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)