Properties

Label 1638.2.a
Level $1638$
Weight $2$
Character orbit 1638.a
Rep. character $\chi_{1638}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $25$
Sturm bound $672$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(672\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1638))\).

Total New Old
Modular forms 352 30 322
Cusp forms 321 30 291
Eisenstein series 31 0 31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(12\)
Minus space\(-\)\(18\)

Trace form

\( 30q - 2q^{2} + 30q^{4} - 8q^{5} - 2q^{8} + O(q^{10}) \) \( 30q - 2q^{2} + 30q^{4} - 8q^{5} - 2q^{8} - 8q^{11} + 30q^{16} + 4q^{17} + 20q^{19} - 8q^{20} + 4q^{22} + 4q^{23} + 50q^{25} + 12q^{29} + 8q^{31} - 2q^{32} + 12q^{34} + 4q^{35} + 12q^{37} + 4q^{38} + 12q^{41} + 8q^{43} - 8q^{44} + 8q^{46} + 24q^{47} + 30q^{49} + 2q^{50} - 4q^{53} + 8q^{55} - 12q^{58} - 20q^{59} - 56q^{61} + 32q^{62} + 30q^{64} - 4q^{65} + 4q^{68} - 4q^{70} - 16q^{71} - 52q^{73} + 20q^{76} - 44q^{79} - 8q^{80} + 4q^{82} + 12q^{83} - 48q^{85} - 16q^{86} + 4q^{88} + 4q^{89} + 2q^{91} + 4q^{92} + 8q^{95} + 4q^{97} - 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1638))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 13
1638.2.a.a \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots\)
1638.2.a.b \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
1638.2.a.c \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
1638.2.a.d \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
1638.2.a.e \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{13}-q^{14}+\cdots\)
1638.2.a.f \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
1638.2.a.g \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
1638.2.a.h \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1638.2.a.i \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(3\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
1638.2.a.j \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(4\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
1638.2.a.k \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-4\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-4q^{5}-q^{7}+q^{8}-4q^{10}+\cdots\)
1638.2.a.l \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
1638.2.a.m \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-3\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
1638.2.a.n \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1638.2.a.o \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1638.2.a.p \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{13}+q^{14}+\cdots\)
1638.2.a.q \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}-q^{13}+\cdots\)
1638.2.a.r \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1638.2.a.s \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
1638.2.a.t \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(3\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
1638.2.a.u \(2\) \(13.079\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-3\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{7}-q^{8}+\cdots\)
1638.2.a.v \(2\) \(13.079\) \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-\beta q^{5}-q^{7}-q^{8}+\beta q^{10}+\cdots\)
1638.2.a.w \(2\) \(13.079\) \(\Q(\sqrt{41}) \) None \(-2\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
1638.2.a.x \(2\) \(13.079\) \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
1638.2.a.y \(2\) \(13.079\) \(\Q(\sqrt{57}) \) None \(2\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1638))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1638)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(819))\)\(^{\oplus 2}\)