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Properties

Label 845.2.e
Level $845$
Weight $2$
Character orbit 845.e
Rep. character $\chi_{845}(146,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $104$
Newform subspaces $16$
Sturm bound $182$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 16 \)
Sturm bound: \(182\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

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

Total New Old
Modular forms 208 104 104
Cusp forms 152 104 48
Eisenstein series 56 0 56

Trace form

\( 104 q + 2 q^{3} - 54 q^{4} - 6 q^{6} + 2 q^{7} + 12 q^{8} - 56 q^{9} + O(q^{10}) \) \( 104 q + 2 q^{3} - 54 q^{4} - 6 q^{6} + 2 q^{7} + 12 q^{8} - 56 q^{9} + 2 q^{10} + 4 q^{12} - 4 q^{14} - 2 q^{15} - 62 q^{16} + 14 q^{17} - 8 q^{18} - 4 q^{20} - 16 q^{21} + 6 q^{23} + 4 q^{24} + 104 q^{25} + 20 q^{27} - 10 q^{28} - 4 q^{30} + 16 q^{31} - 2 q^{32} - 14 q^{33} + 12 q^{34} + 6 q^{35} - 44 q^{36} + 6 q^{37} - 72 q^{38} - 12 q^{40} + 12 q^{41} + 16 q^{42} - 14 q^{43} - 20 q^{44} + 8 q^{45} + 14 q^{46} - 24 q^{47} + 32 q^{48} - 56 q^{49} + 16 q^{51} - 64 q^{53} + 10 q^{54} + 12 q^{55} + 48 q^{56} - 12 q^{57} + 32 q^{58} + 12 q^{59} + 16 q^{60} + 16 q^{61} + 20 q^{62} + 12 q^{63} + 88 q^{64} - 4 q^{66} - 6 q^{67} + 58 q^{68} - 4 q^{69} + 8 q^{70} - 20 q^{71} + 12 q^{72} + 56 q^{73} + 10 q^{74} + 2 q^{75} - 26 q^{76} - 36 q^{77} - 16 q^{79} - 68 q^{81} + 8 q^{83} - 18 q^{84} - 6 q^{85} - 60 q^{86} - 10 q^{87} + 14 q^{88} - 16 q^{89} - 16 q^{90} - 44 q^{92} - 8 q^{93} + 8 q^{94} + 8 q^{95} - 4 q^{96} - 22 q^{97} - 12 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
845.2.e.a 845.e 13.c $2$ $6.747$ \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
845.2.e.b 845.e 13.c $2$ $6.747$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
845.2.e.c 845.e 13.c $4$ $6.747$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
845.2.e.d 845.e 13.c $4$ $6.747$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-1\) \(-2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
845.2.e.e 845.e 13.c $4$ $6.747$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
845.2.e.f 845.e 13.c $4$ $6.747$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
845.2.e.g 845.e 13.c $4$ $6.747$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(1\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
845.2.e.h 845.e 13.c $4$ $6.747$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.e.i 845.e 13.c $6$ $6.747$ 6.0.954288.1 None \(-1\) \(2\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
845.2.e.j 845.e 13.c $6$ $6.747$ 6.0.64827.1 None \(-1\) \(5\) \(-6\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(2-\beta _{4}-2\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.e.k 845.e 13.c $6$ $6.747$ 6.0.954288.1 None \(1\) \(2\) \(6\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
845.2.e.l 845.e 13.c $6$ $6.747$ 6.0.64827.1 None \(1\) \(5\) \(6\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(2-\beta _{4}-2\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.e.m 845.e 13.c $8$ $6.747$ 8.0.22581504.2 None \(-2\) \(2\) \(-8\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}+\beta _{5})q^{2}+(\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
845.2.e.n 845.e 13.c $8$ $6.747$ 8.0.22581504.2 None \(2\) \(2\) \(8\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{5})q^{2}+(\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
845.2.e.o 845.e 13.c $18$ $6.747$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-3\) \(-7\) \(18\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{3}-\beta _{5}+\beta _{6}-\beta _{7}+\beta _{10}+\cdots)q^{2}+\cdots\)
845.2.e.p 845.e 13.c $18$ $6.747$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(3\) \(-7\) \(-18\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{2}+\cdots\)

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

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