Properties

Label 440.2.y
Level $440$
Weight $2$
Character orbit 440.y
Rep. character $\chi_{440}(81,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $48$
Newform subspaces $4$
Sturm bound $144$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 440.y (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(440, [\chi])\).

Total New Old
Modular forms 320 48 272
Cusp forms 256 48 208
Eisenstein series 64 0 64

Trace form

\( 48 q - 4 q^{3} + O(q^{10}) \) \( 48 q - 4 q^{3} - 4 q^{11} - 4 q^{13} + 16 q^{17} + 14 q^{19} - 16 q^{21} + 16 q^{23} - 12 q^{25} + 14 q^{27} + 12 q^{29} - 12 q^{31} - 26 q^{33} + 8 q^{35} - 8 q^{37} - 44 q^{39} - 6 q^{41} - 60 q^{43} - 40 q^{47} - 46 q^{49} - 34 q^{51} + 48 q^{53} + 16 q^{55} - 14 q^{57} + 26 q^{59} + 48 q^{61} + 48 q^{63} + 44 q^{65} - 12 q^{67} + 64 q^{69} + 68 q^{71} + 52 q^{73} + 6 q^{75} - 36 q^{77} + 36 q^{79} - 62 q^{81} + 42 q^{83} - 4 q^{85} + 40 q^{87} - 48 q^{89} - 14 q^{91} + 16 q^{93} - 50 q^{97} + 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(440, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.2.y.a 440.y 11.c $8$ $3.513$ 8.0.13140625.1 None 440.2.y.a \(0\) \(1\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}-\beta _{5})q^{3}+\beta _{7}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
440.2.y.b 440.y 11.c $12$ $3.513$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 440.2.y.b \(0\) \(-1\) \(3\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{4})q^{3}+(1-\beta _{6}+\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots\)
440.2.y.c 440.y 11.c $12$ $3.513$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 440.2.y.c \(0\) \(-1\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{3}+\beta _{8})q^{3}-\beta _{6}q^{5}+(1+\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)
440.2.y.d 440.y 11.c $16$ $3.513$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 440.2.y.d \(0\) \(-3\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(440, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)