Properties

Label 845.2.t
Level $845$
Weight $2$
Character orbit 845.t
Rep. character $\chi_{845}(188,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $268$
Newform subspaces $9$
Sturm bound $182$
Trace bound $6$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.t (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 9 \)
Sturm bound: \(182\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 420 348 72
Cusp forms 308 268 40
Eisenstein series 112 80 32

Trace form

\( 268 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 8 q^{6} + 2 q^{7} - 12 q^{9} + O(q^{10}) \) \( 268 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 8 q^{6} + 2 q^{7} - 12 q^{9} + 2 q^{10} + 16 q^{11} + 40 q^{12} + 20 q^{15} - 70 q^{16} - 4 q^{17} + 20 q^{19} - 4 q^{21} - 24 q^{22} + 6 q^{23} - 32 q^{24} - 26 q^{25} - 76 q^{27} - 18 q^{28} - 22 q^{30} - 48 q^{32} - 18 q^{33} - 2 q^{34} - 52 q^{35} - 36 q^{36} + 4 q^{37} + 8 q^{38} - 48 q^{40} - 10 q^{41} - 28 q^{42} - 22 q^{43} + 36 q^{44} - 4 q^{46} + 40 q^{47} + 144 q^{48} - 10 q^{49} - 36 q^{50} - 30 q^{53} + 48 q^{54} + 10 q^{55} + 16 q^{59} - 28 q^{60} + 24 q^{61} + 32 q^{62} + 36 q^{63} + 28 q^{64} - 32 q^{66} - 18 q^{67} + 74 q^{68} + 24 q^{69} + 12 q^{70} + 16 q^{71} - 4 q^{72} - 18 q^{74} + 54 q^{75} + 64 q^{76} + 60 q^{77} + 2 q^{80} - 50 q^{81} - 112 q^{82} - 48 q^{83} + 40 q^{84} + 26 q^{85} - 60 q^{86} - 54 q^{87} - 98 q^{88} + 6 q^{89} - 350 q^{90} - 72 q^{92} - 32 q^{93} + 48 q^{94} + 30 q^{95} - 56 q^{96} - 66 q^{97} + 30 q^{98} - 60 q^{99} + O(q^{100}) \)

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.t.a 845.t 65.t $4$ $6.747$ \(\Q(\zeta_{12})\) None 65.2.f.a \(0\) \(-2\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
845.2.t.b 845.t 65.t $4$ $6.747$ \(\Q(\zeta_{12})\) None 65.2.f.a \(0\) \(-2\) \(8\) \(-4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
845.2.t.c 845.t 65.t $16$ $6.747$ 16.0.\(\cdots\).1 None 65.2.f.b \(0\) \(6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{5}+\beta _{6}-\beta _{8}+\beta _{9})q^{2}+(1+\beta _{2}+\cdots)q^{3}+\cdots\)
845.2.t.d 845.t 65.t $16$ $6.747$ 16.0.\(\cdots\).1 None 65.2.f.b \(0\) \(6\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{5}+\beta _{6}-\beta _{8}+\beta _{9})q^{2}+(1+\beta _{4}+\cdots)q^{3}+\cdots\)
845.2.t.e 845.t 65.t $20$ $6.747$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 65.2.o.a \(-6\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{4}+\beta _{8}-\beta _{12}-\beta _{14}+\cdots)q^{3}+\cdots\)
845.2.t.f 845.t 65.t $20$ $6.747$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 65.2.o.a \(6\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
845.2.t.g 845.t 65.t $20$ $6.747$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 65.2.o.a \(6\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{2}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{8}+\beta _{12}+\cdots)q^{3}+\cdots\)
845.2.t.h 845.t 65.t $24$ $6.747$ None 845.2.f.c \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
845.2.t.i 845.t 65.t $144$ $6.747$ None 845.2.f.f \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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