Properties

Label 3380.2.f
Level $3380$
Weight $2$
Character orbit 3380.f
Rep. character $\chi_{3380}(3041,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $10$
Sturm bound $1092$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3380.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(1092\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3380, [\chi])\).

Total New Old
Modular forms 588 50 538
Cusp forms 504 50 454
Eisenstein series 84 0 84

Trace form

\( 50q + 50q^{9} + O(q^{10}) \) \( 50q + 50q^{9} - 4q^{17} + 12q^{23} - 50q^{25} - 12q^{27} + 16q^{29} - 12q^{43} - 50q^{49} + 4q^{51} + 16q^{53} - 16q^{55} + 12q^{61} - 4q^{69} + 28q^{77} + 28q^{79} + 82q^{81} + 44q^{87} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3380, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3380.2.f.a \(2\) \(26.989\) \(\Q(\sqrt{-1}) \) None \(0\) \(-6\) \(0\) \(0\) \(q-3q^{3}-iq^{5}+3iq^{7}+6q^{9}+3iq^{11}+\cdots\)
3380.2.f.b \(2\) \(26.989\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-2q^{3}+iq^{5}+2iq^{7}+q^{9}-2iq^{15}+\cdots\)
3380.2.f.c \(2\) \(26.989\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+iq^{5}+5iq^{7}-2q^{9}-5iq^{11}+\cdots\)
3380.2.f.d \(2\) \(26.989\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-iq^{5}+iq^{7}-2q^{9}-3iq^{11}+\cdots\)
3380.2.f.e \(2\) \(26.989\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-iq^{5}-iq^{7}-2q^{9}+3iq^{11}+\cdots\)
3380.2.f.f \(2\) \(26.989\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) \(q+2q^{3}+iq^{5}+2iq^{7}+q^{9}+4iq^{11}+\cdots\)
3380.2.f.g \(6\) \(26.989\) 6.0.153664.1 None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{4}q^{3}+\beta _{5}q^{5}-\beta _{1}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
3380.2.f.h \(6\) \(26.989\) 6.0.5089536.1 None \(0\) \(4\) \(0\) \(0\) \(q+(1+\beta _{3})q^{3}+\beta _{4}q^{5}+(\beta _{4}+\beta _{5})q^{7}+\cdots\)
3380.2.f.i \(8\) \(26.989\) 8.0.22581504.2 None \(0\) \(4\) \(0\) \(0\) \(q+(\beta _{2}-\beta _{4})q^{3}-\beta _{5}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
3380.2.f.j \(18\) \(26.989\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{14}q^{5}+(-\beta _{7}+\beta _{10}-\beta _{16}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1690, [\chi])\)\(^{\oplus 2}\)