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Properties

Label 370.2.w
Level $370$
Weight $2$
Character orbit 370.w
Rep. character $\chi_{370}(21,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $84$
Newform subspaces $2$
Sturm bound $114$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.w (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(114\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 372 84 288
Cusp forms 324 84 240
Eisenstein series 48 0 48

Trace form

\( 84 q + 24 q^{7} + O(q^{10}) \) \( 84 q + 24 q^{7} - 6 q^{10} - 12 q^{13} + 18 q^{14} + 30 q^{19} + 36 q^{21} + 12 q^{28} - 36 q^{29} + 24 q^{33} - 36 q^{34} + 12 q^{35} - 108 q^{36} - 36 q^{37} + 48 q^{38} - 84 q^{39} - 12 q^{41} - 84 q^{42} - 6 q^{44} + 72 q^{45} - 6 q^{46} - 12 q^{47} - 12 q^{49} + 24 q^{52} - 12 q^{55} + 60 q^{62} + 12 q^{63} + 42 q^{64} + 6 q^{65} - 24 q^{67} - 36 q^{69} + 60 q^{71} - 24 q^{73} + 36 q^{74} + 30 q^{76} - 84 q^{77} + 12 q^{78} + 36 q^{79} + 48 q^{83} + 12 q^{85} + 36 q^{86} - 96 q^{87} + 18 q^{89} - 24 q^{90} - 18 q^{91} - 12 q^{92} - 6 q^{94} - 48 q^{95} + 72 q^{97} - 48 q^{98} + 30 q^{99} + O(q^{100}) \)

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.w.a 370.w 37.h $36$ $2.954$ None 370.2.w.a \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{18}]$
370.2.w.b 370.w 37.h $48$ $2.954$ None 370.2.w.b \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{18}]$

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

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