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Properties

Label 444.2.i
Level $444$
Weight $2$
Character orbit 444.i
Rep. character $\chi_{444}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $3$
Sturm bound $152$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 444.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(152\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(444, [\chi])\).

Total New Old
Modular forms 164 12 152
Cusp forms 140 12 128
Eisenstein series 24 0 24

Trace form

\( 12 q - 2 q^{5} - 6 q^{9} + O(q^{10}) \) \( 12 q - 2 q^{5} - 6 q^{9} + 8 q^{11} + 4 q^{13} - 6 q^{17} - 6 q^{19} + 6 q^{21} - 4 q^{23} - 12 q^{25} + 12 q^{29} - 8 q^{31} + 6 q^{33} + 10 q^{35} - 8 q^{37} + 4 q^{41} + 20 q^{43} + 4 q^{45} + 12 q^{47} + 12 q^{49} - 12 q^{51} + 30 q^{53} + 20 q^{55} - 4 q^{57} - 4 q^{59} - 30 q^{65} - 2 q^{67} - 24 q^{71} - 52 q^{73} - 8 q^{75} - 4 q^{77} - 26 q^{79} - 6 q^{81} + 8 q^{83} - 36 q^{85} + 10 q^{87} - 14 q^{91} + 2 q^{93} - 6 q^{95} + 8 q^{97} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(444, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
444.2.i.a 444.i 37.c $2$ $3.545$ \(\Q(\sqrt{-3}) \) None 444.2.i.a \(0\) \(1\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{3}-2\zeta_{6}q^{5}+3\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots\)
444.2.i.b 444.i 37.c $4$ $3.545$ \(\Q(\sqrt{-3}, \sqrt{37})\) None 444.2.i.b \(0\) \(2\) \(1\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}-3\beta _{2}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
444.2.i.c 444.i 37.c $6$ $3.545$ 6.0.27379323.1 None 444.2.i.c \(0\) \(-3\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(444, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(444, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)