Properties

Label 370.2.e
Level $370$
Weight $2$
Character orbit 370.e
Rep. character $\chi_{370}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $6$
Sturm bound $114$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(114\)
Trace bound: \(3\)
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 120 20 100
Cusp forms 104 20 84
Eisenstein series 16 0 16

Trace form

\( 20q + 4q^{3} - 10q^{4} - 8q^{7} - 2q^{9} + O(q^{10}) \) \( 20q + 4q^{3} - 10q^{4} - 8q^{7} - 2q^{9} - 4q^{10} + 4q^{11} + 4q^{12} - 8q^{13} - 8q^{14} - 10q^{16} + 8q^{17} + 10q^{19} - 16q^{21} - 40q^{23} - 10q^{25} + 4q^{26} + 16q^{27} - 8q^{28} + 16q^{29} + 4q^{30} + 12q^{33} - 12q^{34} + 4q^{36} - 12q^{37} - 32q^{38} - 12q^{39} + 2q^{40} - 4q^{41} - 20q^{42} - 2q^{44} - 32q^{45} + 10q^{46} + 32q^{47} - 8q^{48} - 18q^{49} + 72q^{51} - 8q^{52} + 16q^{53} - 24q^{54} + 12q^{55} + 4q^{56} + 20q^{58} + 26q^{59} + 24q^{61} + 4q^{62} - 32q^{63} + 20q^{64} + 6q^{65} + 56q^{66} - 28q^{67} - 16q^{68} - 20q^{69} + 4q^{70} - 28q^{71} + 40q^{73} + 2q^{74} - 8q^{75} + 10q^{76} + 20q^{77} + 12q^{78} + 20q^{79} - 2q^{81} + 24q^{83} + 32q^{84} + 28q^{86} + 36q^{87} + 30q^{89} + 2q^{90} + 8q^{91} + 20q^{92} + 24q^{93} - 18q^{94} + 40q^{97} - 24q^{98} - 2q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
370.2.e.a \(2\) \(2.954\) \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
370.2.e.b \(2\) \(2.954\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
370.2.e.c \(2\) \(2.954\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{2}+3\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
370.2.e.d \(4\) \(2.954\) \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(-2\) \(0\) \(q+(-1+\zeta_{12})q^{2}+\zeta_{12}q^{3}-\zeta_{12}q^{4}+\cdots\)
370.2.e.e \(4\) \(2.954\) \(\Q(\sqrt{-3}, \sqrt{10})\) None \(2\) \(2\) \(-2\) \(-4\) \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
370.2.e.f \(6\) \(2.954\) 6.0.2696112.1 None \(-3\) \(0\) \(3\) \(-2\) \(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)

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

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