Properties

Label 1476.2.k
Level $1476$
Weight $2$
Character orbit 1476.k
Rep. character $\chi_{1476}(73,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $34$
Newform subspaces $3$
Sturm bound $504$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1476.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(504\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1476, [\chi])\).

Total New Old
Modular forms 528 34 494
Cusp forms 480 34 446
Eisenstein series 48 0 48

Trace form

\( 34 q + O(q^{10}) \) \( 34 q + 2 q^{13} + 6 q^{17} - 6 q^{19} + 4 q^{23} - 30 q^{25} - 14 q^{29} - 14 q^{35} + 4 q^{37} - 6 q^{41} - 14 q^{47} - 18 q^{53} + 2 q^{55} + 20 q^{59} + 48 q^{65} + 8 q^{67} - 2 q^{71} - 10 q^{79} - 44 q^{83} - 12 q^{85} - 2 q^{89} + 54 q^{95} - 18 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1476, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1476.2.k.a 1476.k 41.c $6$ $11.786$ 6.0.5089536.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{4}-\beta _{5})q^{5}+(\beta _{1}+\beta _{2}-\beta _{5})q^{7}+\cdots\)
1476.2.k.b 1476.k 41.c $12$ $11.786$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{10})q^{7}+\beta _{11}q^{11}+\cdots\)
1476.2.k.c 1476.k 41.c $16$ $11.786$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{5}-\beta _{9}q^{7}+(\beta _{3}-\beta _{4}-\beta _{7}-\beta _{10}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1476, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1476, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(123, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(246, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(369, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(492, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(738, [\chi])\)\(^{\oplus 2}\)