Properties

Label 1380.2.i
Level $1380$
Weight $2$
Character orbit 1380.i
Rep. character $\chi_{1380}(1241,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 300 32 268
Cusp forms 276 32 244
Eisenstein series 24 0 24

Trace form

\( 32 q + 4 q^{9} + O(q^{10}) \) \( 32 q + 4 q^{9} + 32 q^{25} - 24 q^{27} + 8 q^{31} - 28 q^{39} + 16 q^{49} + 8 q^{69} - 8 q^{73} + 20 q^{81} - 20 q^{87} - 20 q^{93} + O(q^{100}) \)

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.i.a 1380.i 69.c $16$ $11.019$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{3}-q^{5}-\beta _{8}q^{7}-\beta _{6}q^{9}-\beta _{9}q^{11}+\cdots\)
1380.2.i.b 1380.i 69.c $16$ $11.019$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+q^{5}-\beta _{8}q^{7}+\beta _{2}q^{9}+\beta _{9}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)