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Properties

Label 441.2.o
Level $441$
Weight $2$
Character orbit 441.o
Rep. character $\chi_{441}(146,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $5$
Sturm bound $112$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(112\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(441, [\chi])\).

Total New Old
Modular forms 128 88 40
Cusp forms 96 72 24
Eisenstein series 32 16 16

Trace form

\( 72 q + 6 q^{2} + 34 q^{4} + 16 q^{9} + O(q^{10}) \) \( 72 q + 6 q^{2} + 34 q^{4} + 16 q^{9} - 6 q^{11} - 28 q^{15} - 26 q^{16} - 10 q^{18} + 4 q^{22} - 36 q^{23} - 18 q^{25} - 48 q^{29} - 18 q^{30} + 42 q^{32} - 32 q^{36} + 4 q^{37} + 22 q^{39} + 4 q^{43} + 16 q^{46} + 30 q^{50} + 12 q^{51} + 26 q^{57} - 2 q^{58} + 6 q^{60} - 40 q^{64} + 108 q^{65} - 12 q^{67} + 62 q^{72} - 66 q^{74} - 58 q^{78} - 48 q^{81} - 6 q^{85} - 90 q^{86} - 22 q^{88} - 84 q^{92} - 104 q^{93} + 42 q^{95} - 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.2.o.a 441.o 63.o $2$ $3.521$ \(\Q(\sqrt{-3}) \) None \(3\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.o.b 441.o 63.o $2$ $3.521$ \(\Q(\sqrt{-3}) \) None \(3\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.o.c 441.o 63.o $10$ $3.521$ 10.0.\(\cdots\).1 None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7}-\beta _{8})q^{2}+\cdots\)
441.2.o.d 441.o 63.o $10$ $3.521$ 10.0.\(\cdots\).1 None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7}-\beta _{8})q^{2}+\cdots\)
441.2.o.e 441.o 63.o $48$ $3.521$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)