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Properties

Label 370.2.m
Level $370$
Weight $2$
Character orbit 370.m
Rep. character $\chi_{370}(159,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $4$
Sturm bound $114$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(114\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 120 40 80
Cusp forms 104 40 64
Eisenstein series 16 0 16

Trace form

\( 40 q - 20 q^{4} - 3 q^{5} + 28 q^{9} + O(q^{10}) \) \( 40 q - 20 q^{4} - 3 q^{5} + 28 q^{9} - 6 q^{10} - 12 q^{11} - 12 q^{15} - 20 q^{16} - 6 q^{19} + 3 q^{20} - 13 q^{25} - 4 q^{26} - 8 q^{30} - 6 q^{34} + 48 q^{35} - 56 q^{36} + 12 q^{39} + 3 q^{40} + 14 q^{41} + 6 q^{44} - 10 q^{46} + 28 q^{49} + 3 q^{50} - 60 q^{55} - 30 q^{59} + 6 q^{61} + 40 q^{64} - 4 q^{65} + 36 q^{69} + 12 q^{70} + 4 q^{71} + 50 q^{74} + 16 q^{75} + 6 q^{76} + 12 q^{79} + 28 q^{81} - 10 q^{85} - 20 q^{86} - 60 q^{89} - 11 q^{90} + 12 q^{91} - 42 q^{94} - 4 q^{95} + 74 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
370.2.m.a 370.m 185.l $4$ $2.954$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(-3\) \(-6\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
370.2.m.b 370.m 185.l $4$ $2.954$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(3\) \(-3\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
370.2.m.c 370.m 185.l $16$ $2.954$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-8\) \(3\) \(6\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{1})q^{2}+\beta _{10}q^{3}+\beta _{1}q^{4}+\cdots\)
370.2.m.d 370.m 185.l $16$ $2.954$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(8\) \(-3\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{1})q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}+\beta _{8}q^{5}+\cdots\)

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

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