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Properties

Label 364.2.cf
Level $364$
Weight $2$
Character orbit 364.cf
Rep. character $\chi_{364}(45,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $36$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 364.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(364, [\chi])\).

Total New Old
Modular forms 248 36 212
Cusp forms 200 36 164
Eisenstein series 48 0 48

Trace form

\( 36 q + 6 q^{7} + 16 q^{9} + O(q^{10}) \) \( 36 q + 6 q^{7} + 16 q^{9} - 12 q^{11} - 4 q^{15} - 16 q^{19} + 12 q^{21} + 4 q^{29} + 2 q^{31} - 54 q^{33} - 2 q^{35} + 8 q^{37} + 46 q^{39} + 30 q^{41} + 12 q^{43} + 4 q^{49} - 24 q^{51} - 16 q^{53} + 6 q^{55} + 14 q^{57} - 12 q^{61} + 50 q^{63} - 34 q^{65} - 60 q^{67} - 42 q^{69} + 22 q^{71} - 50 q^{73} - 28 q^{75} + 8 q^{79} - 6 q^{81} + 18 q^{83} - 4 q^{85} + 6 q^{89} - 34 q^{91} - 22 q^{93} + 10 q^{97} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(364, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
364.2.cf.a 364.cf 91.aa $36$ $2.907$ None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(364, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(364, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)