Properties

Label 2205.2.a
Level $2205$
Weight $2$
Character orbit 2205.a
Rep. character $\chi_{2205}(1,\cdot)$
Character field $\Q$
Dimension $69$
Newform subspaces $35$
Sturm bound $672$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 35 \)
Sturm bound: \(672\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(2\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2205))\).

Total New Old
Modular forms 368 69 299
Cusp forms 305 69 236
Eisenstein series 63 0 63

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

\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(32\)
Minus space\(-\)\(37\)

Trace form

\( 69q - 3q^{2} + 67q^{4} + q^{5} - 15q^{8} + O(q^{10}) \) \( 69q - 3q^{2} + 67q^{4} + q^{5} - 15q^{8} - 3q^{10} - 4q^{11} + 6q^{13} + 59q^{16} - 2q^{17} + 4q^{19} - q^{20} + 12q^{22} + 4q^{23} + 69q^{25} - 18q^{26} - 10q^{29} - 12q^{31} - 23q^{32} + 30q^{34} - 18q^{37} + 28q^{38} - 3q^{40} - 10q^{41} - 16q^{43} + 12q^{44} - 28q^{46} + 28q^{47} - 3q^{50} + 38q^{52} - 6q^{53} - 4q^{55} - 2q^{58} - 8q^{59} - 30q^{61} + 24q^{62} + 107q^{64} - 6q^{65} - 16q^{67} - 26q^{68} + 24q^{71} + 6q^{73} + 62q^{74} - 12q^{76} - 48q^{79} - q^{80} + 10q^{82} + 12q^{83} - 14q^{85} + 64q^{86} + 92q^{88} - 22q^{89} + 140q^{92} + 28q^{94} - 20q^{95} + 42q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2205))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 7
2205.2.a.a \(1\) \(17.607\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+2q^{11}+\cdots\)
2205.2.a.b \(1\) \(17.607\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+6q^{13}+\cdots\)
2205.2.a.c \(1\) \(17.607\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+2q^{11}+\cdots\)
2205.2.a.d \(1\) \(17.607\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{4}-q^{5}+q^{13}+4q^{16}+6q^{17}+\cdots\)
2205.2.a.e \(1\) \(17.607\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{4}-q^{5}+3q^{11}-5q^{13}+4q^{16}+\cdots\)
2205.2.a.f \(1\) \(17.607\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q-2q^{4}+q^{5}-q^{13}+4q^{16}-6q^{17}+\cdots\)
2205.2.a.g \(1\) \(17.607\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-2q^{11}+\cdots\)
2205.2.a.h \(1\) \(17.607\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}-2q^{11}+\cdots\)
2205.2.a.i \(1\) \(17.607\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+4q^{11}+\cdots\)
2205.2.a.j \(1\) \(17.607\) \(\Q\) None \(2\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{2}+2q^{4}-q^{5}-2q^{10}-q^{11}+\cdots\)
2205.2.a.k \(1\) \(17.607\) \(\Q\) None \(2\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+6q^{11}+\cdots\)
2205.2.a.l \(1\) \(17.607\) \(\Q\) None \(2\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}-q^{11}+\cdots\)
2205.2.a.m \(1\) \(17.607\) \(\Q\) None \(2\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}+6q^{11}+\cdots\)
2205.2.a.n \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.o \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.p \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.q \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.r \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.s \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+\beta q^{2}-q^{5}-2\beta q^{8}-\beta q^{10}+(-2+\cdots)q^{11}+\cdots\)
2205.2.a.t \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+\beta q^{2}-q^{5}-2\beta q^{8}-\beta q^{10}+(3-2\beta )q^{11}+\cdots\)
2205.2.a.u \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+q^{5}-2\beta q^{8}+\beta q^{10}+(-2+\cdots)q^{11}+\cdots\)
2205.2.a.v \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+q^{5}-2\beta q^{8}+\beta q^{10}+(3-2\beta )q^{11}+\cdots\)
2205.2.a.w \(2\) \(17.607\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+3q^{4}-q^{5}-\beta q^{8}+\beta q^{10}+\cdots\)
2205.2.a.x \(2\) \(17.607\) \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(4+\beta )q^{8}+\cdots\)
2205.2.a.y \(2\) \(17.607\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(3+\beta )q^{8}+\cdots\)
2205.2.a.z \(2\) \(17.607\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+(6+2\beta )q^{8}+\cdots\)
2205.2.a.ba \(2\) \(17.607\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+q^{5}+(6+2\beta )q^{8}+\cdots\)
2205.2.a.bb \(3\) \(17.607\) 3.3.404.1 None \(-2\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.2.a.bc \(3\) \(17.607\) 3.3.404.1 None \(-2\) \(0\) \(3\) \(0\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.2.a.bd \(3\) \(17.607\) 3.3.404.1 None \(2\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
2205.2.a.be \(3\) \(17.607\) 3.3.404.1 None \(2\) \(0\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
2205.2.a.bf \(4\) \(17.607\) 4.4.4352.1 None \(-4\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q+(-1-\beta _{1}+\beta _{3})q^{2}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
2205.2.a.bg \(4\) \(17.607\) 4.4.4352.1 None \(-4\) \(0\) \(4\) \(0\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{1}+\beta _{3})q^{2}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
2205.2.a.bh \(4\) \(17.607\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+\beta _{3}q^{8}-\beta _{1}q^{10}+\cdots\)
2205.2.a.bi \(4\) \(17.607\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+\beta _{3}q^{8}+\beta _{1}q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2205))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2205)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 2}\)