Properties

Label 370.2.o
Level $370$
Weight $2$
Character orbit 370.o
Rep. character $\chi_{370}(71,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $84$
Newform subspaces $4$
Sturm bound $114$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.o (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 4 \)
Sturm bound: \(114\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(370, [\chi])\).

Total New Old
Modular forms 360 84 276
Cusp forms 312 84 228
Eisenstein series 48 0 48

Trace form

\( 84 q - 24 q^{7} + O(q^{10}) \) \( 84 q - 24 q^{7} + 6 q^{10} + 12 q^{13} - 6 q^{14} - 18 q^{19} + 36 q^{21} + 72 q^{23} + 12 q^{28} - 12 q^{29} + 48 q^{31} - 120 q^{33} - 36 q^{34} + 12 q^{35} + 108 q^{36} - 36 q^{37} - 96 q^{38} - 12 q^{39} + 60 q^{41} - 12 q^{42} - 96 q^{43} + 6 q^{44} - 24 q^{45} + 6 q^{46} - 12 q^{47} - 36 q^{49} - 24 q^{52} + 72 q^{54} + 12 q^{55} + 72 q^{57} + 48 q^{61} + 12 q^{62} - 84 q^{63} - 42 q^{64} + 6 q^{65} - 24 q^{67} + 24 q^{68} + 60 q^{69} + 12 q^{71} - 72 q^{73} - 36 q^{74} - 18 q^{76} - 12 q^{77} + 84 q^{78} - 36 q^{79} - 96 q^{81} + 48 q^{82} + 48 q^{83} + 12 q^{85} - 12 q^{86} + 54 q^{89} + 24 q^{90} + 90 q^{91} + 12 q^{92} - 144 q^{93} + 42 q^{94} - 48 q^{95} - 24 q^{97} - 144 q^{98} + 102 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(370, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
370.2.o.a 370.o 37.f $18$ $2.954$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 370.2.o.a \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{8}-\beta _{17})q^{3}+\beta _{6}q^{4}+\cdots\)
370.2.o.b 370.o 37.f $18$ $2.954$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 370.2.o.b \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{10}+\beta _{11})q^{4}+\cdots\)
370.2.o.c 370.o 37.f $24$ $2.954$ None 370.2.o.c \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$
370.2.o.d 370.o 37.f $24$ $2.954$ None 370.2.o.d \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(370, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(370, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)