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Properties

Label 1476.2.n
Level $1476$
Weight $2$
Character orbit 1476.n
Rep. character $\chi_{1476}(37,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $72$
Newform subspaces $7$
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.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 7 \)
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

\( 72 q + O(q^{10}) \) \( 72 q - 5 q^{11} - 4 q^{13} - 9 q^{17} + q^{19} - 4 q^{25} - 20 q^{29} - q^{31} - 31 q^{35} - 14 q^{37} + 26 q^{41} - q^{47} - 70 q^{49} - 5 q^{53} + 34 q^{55} + 32 q^{59} + 6 q^{61} - 12 q^{65} - 17 q^{67} + 31 q^{71} - 26 q^{73} + 17 q^{77} - 6 q^{79} - 8 q^{83} + 54 q^{85} - 12 q^{89} - 28 q^{91} + 12 q^{95} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.n.a 1476.n 41.d $4$ $11.786$ \(\Q(\zeta_{10})\) None \(0\) \(0\) \(-7\) \(9\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-3+3\zeta_{10}+2\zeta_{10}^{3})q^{5}+(3+3\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1476.2.n.b 1476.n 41.d $4$ $11.786$ \(\Q(\zeta_{10})\) None \(0\) \(0\) \(-5\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1476.2.n.c 1476.n 41.d $4$ $11.786$ \(\Q(\zeta_{10})\) None \(0\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1476.2.n.d 1476.n 41.d $4$ $11.786$ \(\Q(\zeta_{10})\) None \(0\) \(0\) \(7\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-2\zeta_{10}+\zeta_{10}^{3})q^{5}+(2-2\zeta_{10}+\cdots)q^{7}+\cdots\)
1476.2.n.e 1476.n 41.d $8$ $11.786$ 8.0.2127515625.1 None \(0\) \(0\) \(2\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{4}q^{5}+(-2+\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
1476.2.n.f 1476.n 41.d $16$ $11.786$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\beta _{3}+\beta _{4}-\beta _{6}-\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1476.2.n.g 1476.n 41.d $32$ $11.786$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$

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

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