Properties

Label 1380.2.f
Level $1380$
Weight $2$
Character orbit 1380.f
Rep. character $\chi_{1380}(829,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
Sturm bound $576$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 300 20 280
Cusp forms 276 20 256
Eisenstein series 24 0 24

Trace form

\( 20q - 20q^{9} + O(q^{10}) \) \( 20q - 20q^{9} + 4q^{15} + 8q^{19} - 8q^{21} - 4q^{25} - 12q^{29} - 20q^{31} - 12q^{35} + 8q^{39} + 36q^{41} + 16q^{49} - 20q^{59} + 24q^{61} - 32q^{65} + 8q^{69} + 28q^{71} - 8q^{75} - 24q^{79} + 20q^{81} - 36q^{85} - 56q^{89} + 32q^{91} - 16q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1380.2.f.a \(6\) \(11.019\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots\)
1380.2.f.b \(14\) \(11.019\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{3}+\beta _{10}q^{5}+\beta _{13}q^{7}-q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)