Properties

Label 1260.2.c
Level $1260$
Weight $2$
Character orbit 1260.c
Rep. character $\chi_{1260}(811,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $6$
Sturm bound $576$
Trace bound $10$

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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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(576\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(11\), \(19\)

Dimensions

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

Total New Old
Modular forms 304 80 224
Cusp forms 272 80 192
Eisenstein series 32 0 32

Trace form

\( 80 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + O(q^{10}) \) \( 80 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 6 q^{14} - 6 q^{16} - 24 q^{22} - 80 q^{25} + 22 q^{28} - 24 q^{29} + 38 q^{32} + 52 q^{44} + 20 q^{46} - 20 q^{49} + 2 q^{50} + 32 q^{53} - 34 q^{56} + 32 q^{58} + 2 q^{64} + 8 q^{65} - 8 q^{70} + 4 q^{74} + 24 q^{77} - 100 q^{86} - 20 q^{88} - 132 q^{92} + 54 q^{98} + O(q^{100}) \)

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.c.a \(4\) \(10.061\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{4}+\cdots\)
1260.2.c.b \(4\) \(10.061\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{4}+\cdots\)
1260.2.c.c \(8\) \(10.061\) 8.0.342102016.5 None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5})q^{4}+\beta _{2}q^{5}+\cdots\)
1260.2.c.d \(16\) \(10.061\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(0\) \(0\) \(-4\) \(q+\beta _{4}q^{2}+\beta _{8}q^{4}+\beta _{3}q^{5}+(-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots\)
1260.2.c.e \(16\) \(10.061\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(0\) \(0\) \(4\) \(q+\beta _{4}q^{2}+\beta _{8}q^{4}-\beta _{3}q^{5}-\beta _{15}q^{7}+\cdots\)
1260.2.c.f \(32\) \(10.061\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)