Properties

Label 2112.2.b
Level $2112$
Weight $2$
Character orbit 2112.b
Rep. character $\chi_{2112}(65,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $22$
Sturm bound $768$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2112.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(768\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\), \(29\), \(31\), \(83\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2112, [\chi])\).

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92 q - 4 q^{9} + O(q^{10}) \) \( 92 q - 4 q^{9} - 84 q^{25} + 12 q^{33} + 8 q^{37} + 8 q^{45} - 76 q^{49} - 32 q^{69} + 12 q^{81} - 8 q^{93} - 40 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2112, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2112.2.b.a \(2\) \(16.864\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
2112.2.b.b \(2\) \(16.864\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1-\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
2112.2.b.c \(2\) \(16.864\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta )q^{3}+\beta q^{5}-\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
2112.2.b.d \(2\) \(16.864\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1-\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
2112.2.b.e \(2\) \(16.864\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\beta )q^{3}+(1-2\beta )q^{5}+(-2-\beta )q^{9}+\cdots\)
2112.2.b.f \(2\) \(16.864\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(0\) \(0\) \(q+(1-\beta )q^{3}+(1-2\beta )q^{5}+(-2-\beta )q^{9}+\cdots\)
2112.2.b.g \(2\) \(16.864\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
2112.2.b.h \(2\) \(16.864\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1-\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1-2\beta )q^{9}+\cdots\)
2112.2.b.i \(2\) \(16.864\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
2112.2.b.j \(2\) \(16.864\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1-\beta )q^{3}+\beta q^{5}-\beta q^{7}+(-1-2\beta )q^{9}+\cdots\)
2112.2.b.k \(4\) \(16.864\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2})q^{9}+\cdots\)
2112.2.b.l \(4\) \(16.864\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-33}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}-3q^{9}-\beta _{3}q^{11}+\cdots\)
2112.2.b.m \(4\) \(16.864\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-33}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}-3q^{9}-\beta _{3}q^{11}+\cdots\)
2112.2.b.n \(4\) \(16.864\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2})q^{9}+\cdots\)
2112.2.b.o \(6\) \(16.864\) 6.0.7388168.1 None \(0\) \(-1\) \(0\) \(0\) \(q-\beta _{4}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
2112.2.b.p \(6\) \(16.864\) 6.0.7388168.1 None \(0\) \(-1\) \(0\) \(0\) \(q-\beta _{4}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
2112.2.b.q \(6\) \(16.864\) 6.0.7388168.1 None \(0\) \(1\) \(0\) \(0\) \(q+\beta _{4}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
2112.2.b.r \(6\) \(16.864\) 6.0.7388168.1 None \(0\) \(1\) \(0\) \(0\) \(q+\beta _{4}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
2112.2.b.s \(8\) \(16.864\) 8.0.121550625.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+(\beta _{4}+\beta _{6})q^{5}-\beta _{5}q^{7}+\beta _{6}q^{9}+\cdots\)
2112.2.b.t \(8\) \(16.864\) 8.0.121550625.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{4}+\beta _{6})q^{5}+\beta _{5}q^{7}+\beta _{6}q^{9}+\cdots\)
2112.2.b.u \(8\) \(16.864\) 8.0.1544804416.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(-\beta _{5}+\beta _{7})q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
2112.2.b.v \(8\) \(16.864\) 8.0.1544804416.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(-\beta _{5}+\beta _{7})q^{5}+(\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2112, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 2}\)