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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

\( 50q + 4q^{3} - 46q^{4} + 50q^{9} + O(q^{10}) \) \( 50q + 4q^{3} - 46q^{4} + 50q^{9} - 2q^{10} - 12q^{14} + 46q^{16} - 4q^{17} + 20q^{22} - 16q^{23} - 50q^{25} + 28q^{27} - 20q^{30} + 4q^{35} - 2q^{36} + 44q^{38} + 6q^{40} - 64q^{42} - 24q^{43} - 56q^{48} - 50q^{49} - 4q^{51} - 24q^{53} + 8q^{55} + 80q^{56} - 4q^{61} + 8q^{62} - 74q^{64} - 52q^{66} + 64q^{68} + 44q^{69} - 40q^{74} - 4q^{75} - 20q^{77} - 36q^{79} + 18q^{81} + 48q^{82} - 4q^{87} - 48q^{88} + 42q^{90} - 12q^{92} - 4q^{94} - 16q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
845.2.c.a \(2\) \(6.747\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+iq^{2}-2q^{3}+q^{4}+iq^{5}-2iq^{6}+\cdots\)
845.2.c.b \(4\) \(6.747\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{3}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
845.2.c.c \(4\) \(6.747\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+2\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
845.2.c.d \(4\) \(6.747\) \(\Q(i, \sqrt{13})\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
845.2.c.e \(4\) \(6.747\) \(\Q(\zeta_{12})\) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(1-\zeta_{12}^{3})q^{3}-q^{4}+\zeta_{12}q^{5}+\cdots\)
845.2.c.f \(6\) \(6.747\) 6.0.153664.1 None \(0\) \(-10\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
845.2.c.g \(8\) \(6.747\) 8.0.22581504.2 None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.c.h \(18\) \(6.747\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(14\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{6})q^{2}+(1+\beta _{11})q^{3}+(-2+\cdots)q^{4}+\cdots\)

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

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