Properties

Label 3381.2.a
Level $3381$
Weight $2$
Character orbit 3381.a
Rep. character $\chi_{3381}(1,\cdot)$
Character field $\Q$
Dimension $150$
Newform subspaces $38$
Sturm bound $896$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3381.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(896\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3381))\).

Total New Old
Modular forms 464 150 314
Cusp forms 433 150 283
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.

\(3\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(16\)
\(+\)\(+\)\(-\)\(-\)\(20\)
\(+\)\(-\)\(+\)\(-\)\(22\)
\(+\)\(-\)\(-\)\(+\)\(16\)
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(24\)
Plus space\(+\)\(65\)
Minus space\(-\)\(85\)

Trace form

\( 150q - 2q^{2} + 2q^{3} + 150q^{4} - 8q^{5} + 2q^{6} + 6q^{8} + 150q^{9} + O(q^{10}) \) \( 150q - 2q^{2} + 2q^{3} + 150q^{4} - 8q^{5} + 2q^{6} + 6q^{8} + 150q^{9} + 4q^{10} - 2q^{12} + 4q^{13} + 4q^{15} + 158q^{16} - 8q^{17} - 2q^{18} + 8q^{19} + 8q^{20} + 16q^{22} + 18q^{24} + 146q^{25} + 4q^{26} + 2q^{27} - 4q^{29} - 8q^{30} + 24q^{31} - 10q^{32} + 8q^{33} - 4q^{34} + 150q^{36} - 16q^{37} - 28q^{38} - 24q^{39} - 28q^{40} - 12q^{41} - 44q^{43} - 32q^{44} - 8q^{45} - 4q^{46} + 32q^{47} - 2q^{48} - 102q^{50} - 4q^{51} - 4q^{52} - 56q^{53} + 2q^{54} - 8q^{55} - 16q^{57} - 44q^{58} + 24q^{59} + 36q^{60} + 4q^{61} + 238q^{64} - 96q^{65} + 16q^{66} + 12q^{67} + 32q^{68} + 4q^{69} + 56q^{71} + 6q^{72} - 4q^{73} - 28q^{74} - 10q^{75} + 72q^{76} + 20q^{78} + 20q^{79} + 40q^{80} + 150q^{81} - 12q^{82} - 8q^{83} - 80q^{85} + 60q^{86} + 4q^{87} + 64q^{88} - 32q^{89} + 4q^{90} - 12q^{93} - 8q^{94} + 56q^{95} + 18q^{96} + 28q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3381))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 23
3381.2.a.a \(1\) \(26.997\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
3381.2.a.b \(1\) \(26.997\) \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}-q^{4}+3q^{5}+q^{6}+3q^{8}+\cdots\)
3381.2.a.c \(1\) \(26.997\) \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}-3q^{5}-q^{6}+3q^{8}+\cdots\)
3381.2.a.d \(1\) \(26.997\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
3381.2.a.e \(1\) \(26.997\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}+q^{9}-2q^{11}+2q^{12}+\cdots\)
3381.2.a.f \(1\) \(26.997\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}+q^{9}+5q^{11}+2q^{12}+\cdots\)
3381.2.a.g \(1\) \(26.997\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}+q^{9}+6q^{11}+2q^{12}+\cdots\)
3381.2.a.h \(1\) \(26.997\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}+q^{9}-2q^{11}-2q^{12}+\cdots\)
3381.2.a.i \(1\) \(26.997\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}+q^{9}+5q^{11}-2q^{12}+\cdots\)
3381.2.a.j \(1\) \(26.997\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{3}-2q^{4}+q^{9}+6q^{11}-2q^{12}+\cdots\)
3381.2.a.k \(1\) \(26.997\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
3381.2.a.l \(1\) \(26.997\) \(\Q\) None \(2\) \(-1\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots\)
3381.2.a.m \(1\) \(26.997\) \(\Q\) None \(2\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{9}+q^{11}+\cdots\)
3381.2.a.n \(2\) \(26.997\) \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(5\) \(0\) \(+\) \(-\) \(+\) \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(2+\beta )q^{5}+\cdots\)
3381.2.a.o \(2\) \(26.997\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-5\) \(0\) \(+\) \(-\) \(-\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots\)
3381.2.a.p \(2\) \(26.997\) \(\Q(\sqrt{13}) \) None \(-1\) \(-2\) \(5\) \(0\) \(+\) \(-\) \(-\) \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+(3-\beta )q^{5}+\cdots\)
3381.2.a.q \(2\) \(26.997\) \(\Q(\sqrt{17}) \) None \(-1\) \(-2\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+\beta q^{5}+\beta q^{6}+\cdots\)
3381.2.a.r \(2\) \(26.997\) \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
3381.2.a.s \(2\) \(26.997\) \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-\beta q^{5}-\beta q^{6}+\cdots\)
3381.2.a.t \(2\) \(26.997\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q-\beta q^{2}+q^{3}+3q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots\)
3381.2.a.u \(2\) \(26.997\) \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
3381.2.a.v \(3\) \(26.997\) 3.3.837.1 None \(0\) \(-3\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
3381.2.a.w \(4\) \(26.997\) 4.4.24197.1 None \(0\) \(4\) \(-5\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
3381.2.a.x \(4\) \(26.997\) 4.4.15317.1 None \(2\) \(4\) \(-5\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
3381.2.a.y \(5\) \(26.997\) 5.5.3176240.1 None \(1\) \(-5\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
3381.2.a.z \(5\) \(26.997\) 5.5.3176240.1 None \(1\) \(5\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
3381.2.a.ba \(6\) \(26.997\) 6.6.62622704.1 None \(-3\) \(-6\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
3381.2.a.bb \(6\) \(26.997\) 6.6.62622704.1 None \(-3\) \(6\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
3381.2.a.bc \(6\) \(26.997\) 6.6.7997584.1 None \(-1\) \(-6\) \(3\) \(0\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots\)
3381.2.a.bd \(6\) \(26.997\) 6.6.7997584.1 None \(-1\) \(6\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
3381.2.a.be \(8\) \(26.997\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-8\) \(-5\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{7})q^{5}+\cdots\)
3381.2.a.bf \(8\) \(26.997\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(8\) \(5\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{7})q^{5}+\cdots\)
3381.2.a.bg \(10\) \(26.997\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(-10\) \(4\) \(0\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
3381.2.a.bh \(10\) \(26.997\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(10\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots\)
3381.2.a.bi \(10\) \(26.997\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(-10\) \(-5\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{8}+\cdots)q^{5}+\cdots\)
3381.2.a.bj \(10\) \(26.997\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(10\) \(5\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{8}+\cdots)q^{5}+\cdots\)
3381.2.a.bk \(10\) \(26.997\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(-10\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
3381.2.a.bl \(10\) \(26.997\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(10\) \(4\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3381))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3381)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1127))\)\(^{\oplus 2}\)