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Properties

Label 370.2.b
Level $370$
Weight $2$
Character orbit 370.b
Rep. character $\chi_{370}(149,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $4$
Sturm bound $114$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(114\)
Trace bound: \(5\)
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 62 18 44
Cusp forms 54 18 36
Eisenstein series 8 0 8

Trace form

\( 18 q - 18 q^{4} - 4 q^{5} - 6 q^{9} + O(q^{10}) \) \( 18 q - 18 q^{4} - 4 q^{5} - 6 q^{9} - 4 q^{10} - 4 q^{14} + 18 q^{16} - 20 q^{19} + 4 q^{20} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 20 q^{30} + 8 q^{31} + 16 q^{35} + 6 q^{36} - 40 q^{39} + 4 q^{40} - 4 q^{41} + 20 q^{45} - 12 q^{46} - 54 q^{49} + 8 q^{50} + 8 q^{51} + 36 q^{55} + 4 q^{56} + 20 q^{59} - 18 q^{64} - 8 q^{66} - 80 q^{69} + 24 q^{71} - 10 q^{74} + 50 q^{75} + 20 q^{76} - 48 q^{79} - 4 q^{80} - 14 q^{81} - 8 q^{84} + 36 q^{85} - 4 q^{86} - 60 q^{89} + 50 q^{90} + 48 q^{91} - 36 q^{94} + 36 q^{95} + 4 q^{99} + O(q^{100}) \)

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.b.a 370.b 5.b $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2-i)q^{5}-2iq^{7}+\cdots\)
370.2.b.b 370.b 5.b $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots\)
370.2.b.c 370.b 5.b $4$ $2.954$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
370.2.b.d 370.b 5.b $10$ $2.954$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{4}-\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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