Properties

Label 370.2.n
Level $370$
Weight $2$
Character orbit 370.n
Rep. character $\chi_{370}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $6$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
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 36 88
Cusp forms 108 36 72
Eisenstein series 16 0 16

Trace form

\( 36q + 18q^{4} + 4q^{5} + 18q^{9} + O(q^{10}) \) \( 36q + 18q^{4} + 4q^{5} + 18q^{9} + 4q^{10} - 12q^{11} - 8q^{14} - 18q^{16} + 14q^{19} - 4q^{20} + 16q^{21} - 10q^{25} - 12q^{26} + 16q^{29} - 8q^{30} - 32q^{31} - 12q^{34} + 8q^{35} + 36q^{36} - 20q^{39} + 2q^{40} + 4q^{41} - 6q^{44} + 64q^{45} - 6q^{46} - 6q^{49} - 32q^{50} - 8q^{51} - 12q^{55} - 4q^{56} + 46q^{59} - 24q^{61} - 36q^{64} - 30q^{65} + 8q^{66} - 52q^{69} + 12q^{70} + 36q^{71} - 2q^{74} + 16q^{75} - 14q^{76} + 12q^{79} - 8q^{80} - 34q^{81} + 32q^{84} - 24q^{85} + 28q^{86} - 30q^{89} - 14q^{90} - 6q^{94} + 24q^{95} - 94q^{99} + O(q^{100}) \)

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.n.a \(4\) \(2.954\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-8\) \(-6\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}^{3})q^{5}+\cdots\)
370.2.n.b \(4\) \(2.954\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
370.2.n.c \(4\) \(2.954\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(6\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
370.2.n.d \(4\) \(2.954\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
370.2.n.e \(8\) \(2.954\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-2\beta _{5}q^{3}-\beta _{4}q^{4}+(\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
370.2.n.f \(12\) \(2.954\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(\beta _{5}-\beta _{6}-\beta _{7}+\beta _{9})q^{3}+\cdots\)

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

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