Properties

Label 2366.2.d
Level $2366$
Weight $2$
Character orbit 2366.d
Rep. character $\chi_{2366}(337,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $18$
Sturm bound $728$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2366.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(728\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2366, [\chi])\).

Total New Old
Modular forms 392 76 316
Cusp forms 336 76 260
Eisenstein series 56 0 56

Trace form

\( 76q - 76q^{4} + 64q^{9} + O(q^{10}) \) \( 76q - 76q^{4} + 64q^{9} + 8q^{10} - 4q^{14} + 76q^{16} + 8q^{17} - 4q^{22} - 16q^{23} - 72q^{25} + 24q^{27} - 12q^{29} - 8q^{30} + 4q^{35} - 64q^{36} + 16q^{38} - 8q^{40} - 4q^{42} - 28q^{43} - 76q^{49} + 8q^{51} + 12q^{53} - 40q^{55} + 4q^{56} + 16q^{61} - 24q^{62} - 76q^{64} + 48q^{66} - 8q^{68} - 32q^{69} + 4q^{74} + 80q^{75} + 24q^{77} + 56q^{79} + 52q^{81} - 48q^{82} - 80q^{87} + 4q^{88} - 48q^{90} + 16q^{92} - 32q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2366, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2366.2.d.a \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-iq^{2}-2q^{3}-q^{4}-3iq^{5}+2iq^{6}+\cdots\)
2366.2.d.b \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-iq^{2}-2q^{3}-q^{4}+2iq^{6}-iq^{7}+\cdots\)
2366.2.d.c \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-iq^{2}-2q^{3}-q^{4}+iq^{5}+2iq^{6}+\cdots\)
2366.2.d.d \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-2iq^{5}-iq^{7}+iq^{8}+\cdots\)
2366.2.d.e \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{7}-iq^{8}+\cdots\)
2366.2.d.f \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}-3iq^{5}+iq^{6}+\cdots\)
2366.2.d.g \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}-4iq^{5}+iq^{6}+\cdots\)
2366.2.d.h \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(6\) \(0\) \(0\) \(q-iq^{2}+3q^{3}-q^{4}-3iq^{5}-3iq^{6}+\cdots\)
2366.2.d.i \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(6\) \(0\) \(0\) \(q-iq^{2}+3q^{3}-q^{4}-3iq^{6}-iq^{7}+\cdots\)
2366.2.d.j \(2\) \(18.893\) \(\Q(\sqrt{-1}) \) None \(0\) \(6\) \(0\) \(0\) \(q-iq^{2}+3q^{3}-q^{4}+4iq^{5}-3iq^{6}+\cdots\)
2366.2.d.k \(4\) \(18.893\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+(-1+\zeta_{12}^{3})q^{3}-q^{4}+\cdots\)
2366.2.d.l \(4\) \(18.893\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}+(2\zeta_{12}+\cdots)q^{5}+\cdots\)
2366.2.d.m \(6\) \(18.893\) 6.0.153664.1 None \(0\) \(-10\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-2+\beta _{4})q^{3}-q^{4}-2\beta _{3}q^{5}+\cdots\)
2366.2.d.n \(6\) \(18.893\) 6.0.153664.1 None \(0\) \(-8\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-1-\beta _{2})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2366.2.d.o \(6\) \(18.893\) 6.0.153664.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(-1+\beta _{2}+2\beta _{4})q^{3}-q^{4}+\cdots\)
2366.2.d.p \(6\) \(18.893\) 6.0.153664.1 None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(1-\beta _{4})q^{3}-q^{4}+(2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
2366.2.d.q \(12\) \(18.893\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{8}q^{2}-\beta _{11}q^{3}-q^{4}+(-\beta _{2}-\beta _{9}+\cdots)q^{5}+\cdots\)
2366.2.d.r \(12\) \(18.893\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{7}q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2366, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)