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Properties

Label 441.2.e
Level $441$
Weight $2$
Character orbit 441.e
Rep. character $\chi_{441}(226,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $30$
Newform subspaces $10$
Sturm bound $112$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(112\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(5\), \(13\)

Dimensions

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

Total New Old
Modular forms 144 38 106
Cusp forms 80 30 50
Eisenstein series 64 8 56

Trace form

\( 30 q - 3 q^{2} - 15 q^{4} + 2 q^{5} + 18 q^{8} - 4 q^{10} + 2 q^{11} + 12 q^{13} - 11 q^{16} - 6 q^{19} - 8 q^{20} - 8 q^{22} - 9 q^{25} - 2 q^{26} + 28 q^{29} + 2 q^{31} - q^{32} - 12 q^{37} - 2 q^{38}+ \cdots - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.2.e.a 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) None 21.2.a.a \(-1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-2\zeta_{6}q^{5}-3q^{8}+\cdots\)
441.2.e.b 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) None 21.2.a.a \(-1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+2\zeta_{6}q^{5}-3q^{8}+\cdots\)
441.2.e.c 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 63.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+(2-2\zeta_{6})q^{4}+7q^{13}-4\zeta_{6}q^{16}+\cdots\)
441.2.e.d 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) 49.2.a.a \(1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+3q^{8}+(4-4\zeta_{6})q^{11}+\cdots\)
441.2.e.e 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) None 21.2.e.a \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
441.2.e.f 441.e 7.c $4$ $3.521$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 147.2.a.d \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.e.g 441.e 7.c $4$ $3.521$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 147.2.a.d \(-2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.e.h 441.e 7.c $4$ $3.521$ \(\Q(\sqrt{-3}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) 441.2.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+\beta _{1}q^{2}+5\beta _{2}q^{4}+3\beta _{3}q^{8}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
441.2.e.i 441.e 7.c $4$ $3.521$ \(\Q(\zeta_{12})\) None 63.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta_{2} q^{2}+(\beta_1-1)q^{4}-2\beta_{2} q^{5}+\cdots\)
441.2.e.j 441.e 7.c $4$ $3.521$ \(\Q(\zeta_{12})\) None 63.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta_{2} q^{2}+(\beta_1-1)q^{4}+2\beta_{2} q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(441, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)