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Properties

Label 370.2.l
Level $370$
Weight $2$
Character orbit 370.l
Rep. character $\chi_{370}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $3$
Sturm bound $114$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(114\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 124 20 104
Cusp forms 108 20 88
Eisenstein series 16 0 16

Trace form

\( 20 q + 4 q^{3} + 10 q^{4} + 8 q^{7} - 2 q^{9} + O(q^{10}) \) \( 20 q + 4 q^{3} + 10 q^{4} + 8 q^{7} - 2 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} + 24 q^{13} - 10 q^{16} + 6 q^{19} - 8 q^{21} + 10 q^{25} + 4 q^{26} - 32 q^{27} - 8 q^{28} + 4 q^{30} - 28 q^{33} - 12 q^{34} - 12 q^{35} - 4 q^{36} - 28 q^{37} + 16 q^{38} + 36 q^{39} + 2 q^{40} + 4 q^{41} + 12 q^{42} + 2 q^{44} - 2 q^{46} - 16 q^{47} - 8 q^{48} + 14 q^{49} + 24 q^{52} - 8 q^{53} + 12 q^{55} + 20 q^{58} - 18 q^{59} + 4 q^{62} - 16 q^{63} - 20 q^{64} + 6 q^{65} + 28 q^{67} - 36 q^{69} - 4 q^{70} - 20 q^{71} - 24 q^{73} + 34 q^{74} + 8 q^{75} + 6 q^{76} - 4 q^{77} - 28 q^{78} + 12 q^{79} + 30 q^{81} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 28 q^{86} - 12 q^{87} - 18 q^{89} - 2 q^{90} - 12 q^{91} + 12 q^{92} + 48 q^{93} - 30 q^{94} - 24 q^{98} + 22 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.l.a 370.l 37.e $4$ $2.954$ \(\Q(\zeta_{12})\) None 370.2.l.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
370.2.l.b 370.l 37.e $4$ $2.954$ \(\Q(\zeta_{12})\) None 370.2.l.b \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
370.2.l.c 370.l 37.e $12$ $2.954$ 12.0.\(\cdots\).2 None 370.2.l.c \(0\) \(4\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(1-\beta _{6}+\beta _{10})q^{3}+(1-\beta _{6}+\cdots)q^{4}+\cdots\)

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

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