Properties

Label 2280.2.j
Level $2280$
Weight $2$
Character orbit 2280.j
Rep. character $\chi_{2280}(1369,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $9$
Sturm bound $960$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2280.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(960\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2280, [\chi])\).

Total New Old
Modular forms 496 56 440
Cusp forms 464 56 408
Eisenstein series 32 0 32

Trace form

\( 56q - 8q^{5} - 56q^{9} + O(q^{10}) \) \( 56q - 8q^{5} - 56q^{9} - 4q^{15} + 12q^{19} - 4q^{25} + 32q^{29} - 12q^{35} + 8q^{39} - 32q^{41} + 8q^{45} - 48q^{49} - 12q^{55} - 8q^{61} - 8q^{65} - 16q^{75} + 56q^{81} + 28q^{85} + 48q^{89} + 32q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2280, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2280.2.j.a \(2\) \(18.206\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2+i)q^{5}+4iq^{7}-q^{9}+\cdots\)
2280.2.j.b \(2\) \(18.206\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1+2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2280.2.j.c \(2\) \(18.206\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2280.2.j.d \(2\) \(18.206\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2280.2.j.e \(2\) \(18.206\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1-2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
2280.2.j.f \(6\) \(18.206\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
2280.2.j.g \(10\) \(18.206\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{6}q^{3}+(1-\beta _{2}-\beta _{4})q^{5}+(\beta _{6}+\beta _{9})q^{7}+\cdots\)
2280.2.j.h \(12\) \(18.206\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+\beta _{10}q^{5}+\beta _{2}q^{7}-q^{9}-\beta _{8}q^{11}+\cdots\)
2280.2.j.i \(18\) \(18.206\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{9}q^{3}+\beta _{2}q^{5}-\beta _{5}q^{7}-q^{9}-\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 2}\)