Properties

Label 1476.2.bb
Level $1476$
Weight $2$
Character orbit 1476.bb
Rep. character $\chi_{1476}(433,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $72$
Newform subspaces $4$
Sturm bound $504$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1476.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 4 \)
Sturm bound: \(504\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 1056 72 984
Cusp forms 960 72 888
Eisenstein series 96 0 96

Trace form

\( 72 q + O(q^{10}) \) \( 72 q + 5 q^{11} + 5 q^{17} + 15 q^{19} - 6 q^{23} - 40 q^{25} - q^{31} + 5 q^{35} - 36 q^{37} - 18 q^{41} - 10 q^{43} - 15 q^{47} + 26 q^{49} - 25 q^{53} - 32 q^{59} + 10 q^{61} - 10 q^{65} + 75 q^{67} + 45 q^{71} - 42 q^{73} - 27 q^{77} + 32 q^{83} + 20 q^{89} - 80 q^{91} + 70 q^{95} - 70 q^{97} + O(q^{100}) \)

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.bb.a 1476.bb 41.f $8$ $11.786$ 8.0.26265625.1 None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\beta _{2}-\beta _{7})q^{5}+(2+2\beta _{1})q^{7}+(2\beta _{2}+\cdots)q^{11}+\cdots\)
1476.2.bb.b 1476.bb 41.f $16$ $11.786$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{12}q^{5}+(-\beta _{9}+\beta _{14})q^{7}+(\beta _{3}+\beta _{5}+\cdots)q^{11}+\cdots\)
1476.2.bb.c 1476.bb 41.f $24$ $11.786$ None \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{10}]$
1476.2.bb.d 1476.bb 41.f $24$ $11.786$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

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