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Properties

Label 1380.2.r
Level $1380$
Weight $2$
Character orbit 1380.r
Rep. character $\chi_{1380}(737,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $3$
Sturm bound $576$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(576\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

Total New Old
Modular forms 600 88 512
Cusp forms 552 88 464
Eisenstein series 48 0 48

Trace form

\( 88 q + 8 q^{7} + O(q^{10}) \) \( 88 q + 8 q^{7} + 16 q^{13} + 12 q^{15} + 8 q^{21} - 36 q^{27} - 16 q^{31} - 44 q^{33} + 16 q^{37} + 40 q^{45} + 24 q^{51} - 8 q^{55} + 24 q^{57} + 16 q^{61} - 4 q^{63} + 16 q^{67} - 8 q^{73} - 28 q^{75} - 8 q^{81} - 32 q^{85} + 16 q^{87} - 8 q^{93} - 72 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1380.2.r.a 1380.r 15.e $4$ $11.019$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
1380.2.r.b 1380.r 15.e $4$ $11.019$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
1380.2.r.c 1380.r 15.e $80$ $11.019$ None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)