Properties

Label 1638.2.c
Level $1638$
Weight $2$
Character orbit 1638.c
Rep. character $\chi_{1638}(883,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $11$
Sturm bound $672$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(672\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1638, [\chi])\).

Total New Old
Modular forms 352 36 316
Cusp forms 320 36 284
Eisenstein series 32 0 32

Trace form

\( 36q - 36q^{4} + O(q^{10}) \) \( 36q - 36q^{4} + 4q^{13} - 4q^{14} + 36q^{16} - 8q^{17} + 4q^{22} - 4q^{23} - 20q^{25} - 40q^{29} - 8q^{35} + 32q^{38} - 24q^{43} - 36q^{49} - 4q^{52} - 32q^{53} + 8q^{55} + 4q^{56} - 8q^{61} - 24q^{62} - 36q^{64} + 36q^{65} + 8q^{68} + 4q^{74} - 8q^{77} + 4q^{79} + 16q^{82} - 4q^{88} + 16q^{91} + 4q^{92} - 8q^{94} - 24q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1638, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1638.2.c.a \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots\)
1638.2.c.b \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots\)
1638.2.c.c \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{5}+iq^{7}-iq^{8}+\cdots\)
1638.2.c.d \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots\)
1638.2.c.e \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{5}-iq^{7}+iq^{8}+\cdots\)
1638.2.c.f \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{5}+iq^{7}+iq^{8}+\cdots\)
1638.2.c.g \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+3iq^{5}+iq^{7}+iq^{8}+\cdots\)
1638.2.c.h \(4\) \(13.079\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots\)
1638.2.c.i \(6\) \(13.079\) 6.0.30647296.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots\)
1638.2.c.j \(6\) \(13.079\) 6.0.3356224.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\beta _{1}q^{7}+\cdots\)
1638.2.c.k \(6\) \(13.079\) 6.0.3356224.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}-\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)