Properties

Label 1260.2.f
Level $1260$
Weight $2$
Character orbit 1260.f
Rep. character $\chi_{1260}(629,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $576$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).

Total New Old
Modular forms 312 16 296
Cusp forms 264 16 248
Eisenstein series 48 0 48

Trace form

\( 16 q + O(q^{10}) \) \( 16 q - 16 q^{49} + 64 q^{79} + 16 q^{85} + 32 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1260.2.f.a \(8\) \(10.061\) 8.0.\(\cdots\).11 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+\beta _{5}q^{7}+(\beta _{5}+\beta _{6})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)
1260.2.f.b \(8\) \(10.061\) 8.0.\(\cdots\).11 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)